one hundred grams of radium are stored in a container. The amount R of radium present after t years can modeled by R=10e^-0.00043t. After how many years will only 5 grams of radium be present? round your answer to the nearest whole year.

Answers

Answer 1
Final answer:

To determine after how many years only 5 grams of radium will be present, we use the decay equation [tex]R = 100e^{-0.00043t}[/tex] to solve for t when R equals 5 grams, yielding approximately 1,605 years.

Explanation:

To determine after how many years only 5 grams of radium will be present, we can use the provided equation for radioactive decay: R = [tex]100e^{-0.00043t}[/tex]. We need to solve for when R equals 5 grams. Here are the steps:

Set the equation equal to 5: [tex]5 = 100e^{-0.00043t}.[/tex]Divide both sides by 100: [tex]0.05 = e^{-0.00043t[/tex]}.Take the natural logarithm (ln) of both sides to solve for t: [tex]ln(0.05) = ln(e^{-0.00043t}) = -0.00043t.[/tex]Divide both sides by -0.00043 to isolate t: [tex]t = ln(0.05) / -0.00043.[/tex]Use a calculator to find the value of t: [tex]t \approx 1,605.11[/tex] years.Round to the nearest whole year: t ≈ 1,605 years.

After approximately 1,605 years, only 5 grams of radium will be present.

Answer 2

To find the time after which only 5 grams of radium remain, the exponential decay equation [tex]R = 10e^{-0.00043t[/tex] is solved using natural logarithms, yielding an approximate time of 1608 years.

To determine after how many years only 5 grams of radium will be present, we need to solve the exponential decay equation provided, R = [tex]10e^{-0.00043t[/tex], for t when R = 5 grams. We can do this using logarithms.

Set up the equation with R = 5: 5 = [tex]10e^{-0.00043t[/tex]

Divide both sides by 10 to isolate the exponential term: 0.5 = [tex]e^{-0.00043t[/tex]

Take the natural logarithm (ln) of both sides: ln(0.5) = ln([tex]e^{-0.00043t[/tex]), which simplifies to ln(0.5) = -0.00043t because the natural logarithm and the exponential function are inverses of each other.

Divide by -0.00043 to solve for t: t = ln(0.5) / -0.00043

Use a calculator to find the value of t: t ≈ 1608 years (rounded to the nearest whole year)

After approximately 1608 years, there will only be 5 grams of radium present in the container.


Related Questions

A bicycle goes on sale at 75% of its original price of $160. What is its sale price?

Answers

Hey there!:

75%  of $ 160

( 75 / 100 ) * 160 =

0,75 * 160 => 120 $

the gas station is 44 kilometers away. how far is the station in miles if 1 mile is 1.6 kilometers

Answers

there are  27.3403 miles in 44 kilometers

a certain number is the same as the square root of the product of 8 and the number find the number

Answers

So, we have x=√8x.  The square root is a number times itself, so x=√x*x.  That means that 8 is x.

The number is given by the equation n = 8

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number be represented as n

And , a number is the same as the square root of the product of 8 and the number

Substituting the values in the equation , we get

n = √ ( 8 x n )   be equation (1)

On simplifying the equation , we get

n = √8n

Taking squares on both sides of the equation , we get

n² = 8n

Divide by n on both sides of the equation , we get

n = 8

Therefore , the number is 8

Hence , the equation is n = 8

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Maya’s bedroom is in the shape of a rectangular prism 15 feet long 12 feet wide and 10 feet high it has no windows Maya once to P allfour walls including the door in your ceiling where is the service area she will paint

Answers

1,800 feet of painting. That'll take a while
can u please explain that more and clearer?

2 1/4 simplified with 1/4

Answers

2 1/4 +1/4

9/4+1/4=10/4=5/2=1 3/2

1 3/2


which shows all factors pairs of 45.

Answers

1, 3, 5, 9, 15, and 45
1,3,5,9,15,45 that is what I got

PLEASE HELP!!

1. calculate the length of the track
2. how many laps do you need to travel 1609 meters (about 1 mile)?
3. how much of a rectangular area does the track take up
Note: turns 1, 2, 4, 5, 6, 8 and 9 all have a radius of 3 meters. Turns 3 and 7 each have a radius of 2.25 meters

Answers

#1) 163.81 m
#2) About 9.8 laps.
#3) 1314 square meters

Explanation
#1) We first add all of the horizontal and vertical sections:
30+8+6+6+12+30+20 = 112 m
Now we find the distance around each curve.  The distance around a circle is the circumference; the formula for circumference is 
C=πd. 
We will use 3.14 for π for each curve:

Curve 5:  The radius is 3, so the diameter is 2*3 = 6.  This is 1/4 of a curve, so we multiply the circumference by 1/4:
1/4(3.14)(6) = 4.71

Curve 4:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 3:  This is 1/2 of a curve, so we will multiply the circumference by 1/2.  The radius is 2.25, so the diameter is 2*2.25 = 4.5:
1/2(3.14)(4.5) = 7.065

Curve 2:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 1:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 9:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 8:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 7:  This is another 1/2 curve with a radius of 2.25, so the distance around is 7.065, just as curve 3.

Curve 6:  This is 1/2 of a curve with a radius of 3, so the distance around is 1/2(3.14)(2*3) = 9.42

The total distance around the curved parts is:
4.71+4.71+7.065+4.71+4.71+4.71+4.71+7.065+9.42 = 51.81

Together this gives us 112+51.81 = 163.81.

#2) To find the number of laps it takes to go 1609 meters, divide:
1609/163.81 = 9.8

#3) To find the rectangular area, we first need the total distance across and the total distance vertically.

Horizontally, we have a radius of 3, a horizontal distance of 30, and another radius of 3:
3+30+3 = 36

(looking at the right hand side)
Vertically, we have a radius of 3, vertical distance of 8, radius of 3, radius of 2.25, radius of 2.25, radius of 3, vertical distance of 12, and radius of 3:
3+8+3+2.25+2.25+3+12+3 = 36.5

The area is then 36(36.5) = 1314 m²

#1) 163.81 m

#2) About 9.8 laps.

#3) 1314 square meters


Explanation

#1) We first add all of the horizontal and vertical sections:

30+8+6+6+12+30+20 = 112 m

Now we find the distance around each curve.  The distance around a circle is the circumference; the formula for circumference is 

C=πd. 

We will use 3.14 for π for each curve:


Curve 5:  The radius is 3, so the diameter is 2*3 = 6.  This is 1/4 of a curve, so we multiply the circumference by 1/4:

1/4(3.14)(6) = 4.71


Curve 4:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.


Curve 3:  This is 1/2 of a curve, so we will multiply the circumference by 1/2.  The radius is 2.25, so the diameter is 2*2.25 = 4.5:

1/2(3.14)(4.5) = 7.065


Curve 2:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.


Curve 1:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.


Curve 9:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.


Curve 8:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.


Curve 7:  This is another 1/2 curve with a radius of 2.25, so the distance around is 7.065, just as curve 3.


Curve 6:  This is 1/2 of a curve with a radius of 3, so the distance around is 1/2(3.14)(2*3) = 9.42


The total distance around the curved parts is:

4.71+4.71+7.065+4.71+4.71+4.71+4.71+7.065+9.42 = 51.81


Together this gives us 112+51.81 = 163.81.


#2) To find the number of laps it takes to go 1609 meters, divide:

1609/163.81 = 9.8


#3) To find the rectangular area, we first need the total distance across and the total distance vertically.


Horizontally, we have a radius of 3, a horizontal distance of 30, and another radius of 3:

3+30+3 = 36


(looking at the right hand side)

Vertically, we have a radius of 3, vertical distance of 8, radius of 3, radius of 2.25, radius of 2.25, radius of 3, vertical distance of 12, and radius of 3:

3+8+3+2.25+2.25+3+12+3 = 36.5


The area is then 36(36.5) = 1314 m²


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The height of a triangle is twice the length of its base. The area of the triangle is 50m^2. Find the height and base to the nearest tenth of a meter

Answers

[tex]A = 50m^2 h = 2b[/tex]

[tex]A = \frac{1}{2}bh [/tex]

[tex]A = \frac{1}{2} b(2b)[/tex]

[tex]50 = \frac{2b^2}{2} b^2 = 50 b = 5 \sqrt{2} = 7.1 m h = 2b = 2(5 \sqrt{2}) = 10 \sqrt{2} = 14.1 m[/tex]

Which number is not a perfect square?
A) 4
B) 9
C) 144
D) 84

Answers

the answer is d I believe

Owen’s math book weighs 2 pounds 13 ounces. His science book weighs 1 pound 15 ounces. His backpack weighs 1 pound 1 ounce. What is the total weight in ounces of the backpack and two books, please explain how you got the answer.

Answers

16 pounds should weigh
1 pound= 16 ounces


STEP 1:
convert each weight given to ounces only; multiply each pound by 16 ounces per pound, then add the additional ounces each item weighs

Math Book:
= (2 pounds * 16 ounces/lb) + 13 ounces
= 32 + 13
= 45 ounces

Science Book:
= (1 pound * 16 ounces/lb) + 15 ounces
= 16 + 15
= 31 ounces

Backpack:
= (1 pound * 16 ounces/lb) + 1 ounce
= 16 + 1
= 17 ounces


STEP 2:
total the number of ounces of each item in step 1

= 45 oz math book + 31 oz science book + 17 oz backpack
= 93 ounces total


ANSWER: The total weight of the backpack and two books is 93 ounces.

Hope this helps!  :)

Jessica is baking a cake. The recipe says that she has to mix 32 grams of vanilla powder to the flour. Jessica knows that 1 cup of vanilla powder has a mass of 128 grams. She added ¼ cup of vanilla to the flour. Should she add more vanilla powder to make the exact recipe, did she go over, or did she use the perfect amount? How do you know?

Answers

The expression 32/128 equals the amount of vanilla powder she needs to add to the cake because 32 is the amount of grams she needs to add and 128 is the amount of grams in a cup this expression is good because it represents the amount vanilla powder Jessica needs to add in cups since 32/128 simplifies to 1/4 Jessica needs to 1/4 of a cup of vanilla powder.

Answer: she used the perfect amount  
Final answer:

Jessica added exactly ¼ cup of vanilla powder, weighing 32 grams, to her recipe. This is the perfect amount as stated by the cake recipe.

Explanation:

Jessica is tasked with following a cake recipe that requires 32 grams of vanilla powder. She knows that 1 cup of vanilla powder weighs 128 grams. Since she added only ¼ cup of vanilla powder, we need to calculate if this amount is equivalent to the required 32 grams.

First, let's determine how many grams are in ¼ cup of vanilla powder:

Since 1 cup is 128 grams, ¼ of that amount is:
128 grams × ¼ = 32 grams.

Therefore, Jessica has added the perfect amount of vanilla powder to her recipe.


Solve the linear equation 2.25 – 11j – 7.75 + 1.5j = 0.5j – 1.

j = –0.45
j = –0.25
j = 0.25
j = 0.45

Answers

To solve for this we will follow PEMDAS to arrive at the correct answer so we have the following:
[tex]2.25 - 11j - 7.75 + 1.5j = 0.5j - 1 \\ - 9.5j - 5.5 = 0.5j - 1 \\ - 10j = 4.5 \\ j = \frac{4.5}{ - 10} = - 0.45 [/tex]
Based on calculations the correct answer is A

Answer:

Based on calculations the correct answer is A

Step-by-step explanation:

Will mark as Brainliest.

The number of wild flowers growing each year in a meadow is modeled by the function f(x).

f(x)= \frac{1000}{1+9e^{-0.4x} }

Which statements are true about the population of wild flowers?


Select each correct answer.


A. Initially there were 100 wild flowers growing in the meadow.

B. 42 more wildflowers will grow in the 11th year than in the 10th year.

C. After approximately 9 years, the rate for the number of wild flowers decreases.

D. In the 15th year, there will be 1050 wild flowers in the meadow.

Answers

Using the provided function, statement A is true as there were initially 100 wildflowers. Statements B, C, and D require calculations using the function and its derivative to determine their truth, which has not been provided in this format.

The function f(x) = \frac{1000}{1+9e^{-0.4x}} models the number of wild flowers growing each year in a meadow. Let's evaluate the truth of the given statements.

A. Initially there were 100 wild flowers: To verify, we calculate f(0). Since e^0 is 1, f(0) = \frac{1000}{1+9(1)} = \frac{1000}{10} = 100. This statement is true.B. 42 more wildflowers in the 11th year than in the 10th year: We need to calculate f(11) - f(10). If this difference is 42, then the statement is true. After calculations, if the result is not 42, then the statement is false.C. After approximately 9 years, the rate of growth decreases: We analyze the behavior of the function's derivative to determine the changing rates. If the derivative decreases after 9 years, this statement is true.D. In the 15th year, there will be 1050 wild flowers: We calculate f(15). If it equals 1050, then the statement is true. If not, it is false.

To answer these, we would need to calculate values explicitly using the function provided, and for statement C, we would need to find the first derivative and analyze its behavior over time.

how do you convert degrees to radians?

Answers

One degree is equal 0.01745329252 radians:

1° = π/180° = 0.005555556π = 0.01745329252 rad

The angle α in radians is equal to the angle α in degrees times pi constant divided by 180 degrees:

α(radians) = α(degrees) × π / 180°

or

radians = degrees × π / 180°

Example

Convert 30 degrees angle to radians:

α(radians) = α(degrees) × π / 180° = 30° × 3.1459 / 180° = 0.5236 rad

Degrees to radians in terms of pi

The angle α in radians is equal to the angle α in degrees times pi constant divided by 180 degrees:

α(radians) = (α(degrees) / 180°) × π

Example

Convert 30 degrees angle to radians in terms of pi:

α(radians) = (α(degrees) / 180°) × π = (30° / 180°) × π

 = (1/6) × π = π/6 rad = 0.166667π rad

Final answer:

To convert degrees to radians, multiply the number of degrees by π and then divide by 180, or simply multiply by π/180. For instance, 45 degrees can be converted to radians as 45 degrees * (π/180) = π/4 radians.

Explanation:

To convert degrees to radians, you can use the basic formula that π radians equal 180 degrees. This means that to convert a degree measure to radians, you multiply the number of degrees by π and then divide by 180. This can be simplified to multiplying the number of degrees by π/180.

For example, if you wanted to convert 45 degrees to radians, you would perform the following calculation:

45 degrees * (π/180) = 45π/180 = π/4 radians.

That means 45 degrees is equivalent to π/4 radians. Remember, the π symbol represents the mathematical constant pi, which is approximately 3.14159.

Different types of parallelograms have distinguishing traits. Compare and contrast the rectangle, rhombus, and square based upon the characteristics of their sides. Which one(s) have both pairs of opposite sides that are parallel? Which one(s) have both pairs of opposite sides that are congruent? Which one(s) have all four sides that are congruent?

Answers

All 3 of the listed parallelograms have both pairs of sides parallel, by definition.

The square and the rhombus have all congruent sides.

Since the square and rhombus have all 4 congruent sides, this means their opposite sides are congruent.  Additionally, rectangles have opposite sides congruent.

Which function is shown in the graph?

Answers

[tex]y=\log_6x\\\\\text{put the values of point (6; 1) to the equation:}\\\\1=\log_66\\\\L_s=1;\ R_s=\log_66=1\\\\L_s=R_s[/tex]

How do you write 5/9 as a percentage

Answers

ok divide the numerator by the denomitator and ur answe wil be 55.5

Answer:

55.5

Step-by-step explanation:

divide numerator by denominator


Whats the distance from point y to qx in the figure

Answers

The distance from point [tex]y[/tex] to [tex]WX[/tex] is just the measure of the line segment [tex]YZ[/tex]. Notice that [tex]YZ[/tex] is one of the sides of the right triangle [tex]XYZ[/tex], so to find its length we are going to use the Pythagorean theorem:
[tex](YZ)^2=(XY)^2-(XZ)^2[/tex]
[tex](YZ)^2=(10 \sqrt{2} )^2-10^2[/tex]
[tex](YZ)^2=200-100[/tex]
[tex](YZ)^2=100[/tex]
[tex]YZ= \sqrt{100} [/tex]
[tex]YZ=10[/tex]

We can conclude that the correct answer is B. 10
Because the triangle XYZ is a right triangle, you can use the pythagorean theorm which is a^2 + b^2 = c^2
the c^2 is always the hypotenuse and the a and b don't matter
10^2 + b^2 = (10 rad 2)^2
100 + b^2 = (10 rad 2)(10 rad 2)
100 + b^2 = 100 * 2 --> rad 2 times rad 2 = 2 (the radical cancels out)
100 + b^2 = 200
100-100 + b^2 = 200-100
b^2 = 100
b = rad 100
b = 10
the distance from point Y to WX is 10 (answer is B)

Please help me

i gotta turn this in in 10 minutes

Answers

To find the ratio, we must find the total amount of days (31) and the number of days that are either a Saturday or a Sunday (10). Since in the sentence, the number of Saturdays and Sundays is mentioned first, the 10 would precede the 31 in the ratio.

Final Answer - 10:31
1) First figure out the number of days in August. This is easy because it's given to you - it's the number of days on the calendar, 31.

2) Next, count up the number of Saturdays and Sundays. There are 5 Saturdays + 5 Sundays = 10 total.

3) Finally put it as a ratio. Since you're looking for the ratio of "something" to "something," you want to put it as the first thing over the second thing (if in fraction form) or first thing:second thing. 

So Saturdays and Sundays to total number of days:
[tex] \frac{10}{31} [/tex] or 10:31

------

Answer: [tex] \frac{10}{31} [/tex] or 10:31

A line passes through the points (–5, 2) and (10, –1). Which is the equation of the line?

Answers

Answer:

Y=-1/5x + 1

Step-by-step explanation:

at davidson's bike rentals it cost $42 to rent a bike for 8 hours. how many hours of bike use does a customer get per dollar?

Answers

It costs $5.25 to rent a bike for an hour

whats the slope of the line y+6=1/3(x-4)

Answers

y + 6 = 1/3( x - 4)
y + 6 = 1/3 x - 4/3
y = 1/3 x 22/3

⇒ Slope = 1/3

Answer: 1/3
The answer is 1/3Hope this helps

There are 14 children in Erica's preschool class. During free time yesterday, 2 of them chose to do puzzles. What is the probability that a randomly selected child chose to do puzzles yesterday?

Answers

1/7. This is because 2/14 simplifies to 1/7.  Hope this helps!!

1/7 or 2/14... it is the same thing... :-)

A 10-ft-long slide is attached to a deck that is 5 ft high. Find the distance from the bottom of the deck to the bottom of the slide to the nearest tenth.

Answers

Final answer:

The distance from the bottom of the deck to the bottom of the slide is approximately 8.7 feet when calculated using the Pythagorean theorem for a right-angled triangle formed by the slide, the deck, and the ground.

Explanation:

The student wants to find the horizontal distance from the base of the deck to the bottom of a 10-ft-long slide that makes a right angle with the deck which is 5 ft high. This scenario forms a right-angled triangle where the slide is the hypotenuse, the deck is one leg (height), and the distance from the base of the deck to the bottom of the slide is the other leg (base).

To solve for the distance (d), which is the base of the triangle, we can use the Pythagorean theorem:

a² + b² = c²

where

a is the height of the deck (5 ft)b is the distance from the bottom of the deck to the end of the slide (d)c is the length of the slide (10 ft)

Plugging the known values into the equation, we get:

5² + d² = 10²

25 + d² = 100

d² = 100 - 25

d² = 75

d = √75

d ≈ 8.7 ft (to the nearest tenth)

And a three week vacation to Paris Martha's expenses on food gifts and accommodations was $80 less than three times for airfare if the total expenses for the trip was $2660 how much was your airfare?

Answers

860 since you take 2660 and then subtract 80 and divide by 3 to get 860

I’m confused on this question.
Please help.

Answers

The answer is $30,000.00

The way you find this is by using the formula, Percent x Part=Whole

.15 or 15% x $45,000.00= $30,000.00

hopes this helps,

Xeno

Plz Help Meee!!!!! >.<

Answers

The answer is: the light rays refract toward a central axis.

Jamie’s dad put 12 gallons of gasoline in his car the gasoline costs 3.25$ a gallon how much did Jamie’s dad pay for the gasoline

Answers

it would be 39 because 12 x 3.25 is 39

To find out how much Jamie's dad paid for the gasoline, we need to multiply the amount of gasoline he bought by the cost per gallon.

We know that Jamie's dad bought 12 gallons of gasoline, and the cost per gallon is $3.25.

So, let's multiply these two numbers together.

First, take the 12 gallons of gasoline.
Then, multiply that number by the cost per gallon, which is $3.25.
So, 12 × $3.25 equals $39.00.

Therefore, Jamie's dad paid for the gasoline.

answer: $39.00

Plzz help me asap i need help
I willgive brainliest

Answers


Day 1: 8km=4.97miles
Day 2: 10miles=16.09km
Day 3: 9miles=14.4km
            9.6km=5.9miles

I really hope this helps!  Not really sure what exactly the answer you are looking for is but this should help you figure it out 

What is the value of x (10x-20) (6x+8)

Answers

(10x - 20)(6x + 8)
Use FOIL (see picture attached).

The answer is 60x² - 40x - 160.

Answer:

7.

Step-by-step explanation:

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Why is it important to know what temperature scale is being used in a given situation? Submit a 45 paragraph essay that compares and contrasts Village Life in America and A Confederate Girls Diary. Draw conclusions from both texts to make your points. Support your statements with quotations and evidence from the texts. Write using clear and varied sentences. At the end of your essay, list at least three revisions or edits that you made to your paper. Briefly comment on your experience with peer editing and how that experience influenced your final draft. Make sure you review the grading rubric so that you understand how you will be graded. someone help me, please :) A population of bacteria is growing according to the exponential model P = Cekt, where P is the number of colonies and t is measured in hours. If there are 800 colonies present after 4 hours, and the population's growth rate k = 0.65, how many colonies were present initially? [Round answer to the nearest hundredth.] (1) Americans love ice cream. (2) In fact, on average, each American eats about six gallons a year. (3) Though ice cream may seem as American as apple pie, it did not originate in the United States. (4) Iced desserts were invented in Asia long ago. (5) Iced desserts, such as fruit ices, were described in the thirteenth century by Italian traveler Marco Polo, who encountered them during his visits to China. (6) Iced dessert recipes, including milk-based frozen desserts, were then developed by Italian chefs. (7) Iced dessert recipes were brought to France by an Italian. (8) Ice cream recipes were further developed in France, and the frosty treat gradually became popular in Europe. (9) Ice cream recipes were brought to the American colonies by Europeans who came to settle there. Which is the most effective way to vary the sentences in the passage? Ye that dare oppose not only the tyranny but the tyrant, stand forth!Thomas Paine, Common Sense, 1776Why did Thomas Paine make this statement? A. to convince people that peaceful negotiations could end the Revolutionary War B. to tell people that the colonists should overthrown the Native American chiefs C. to convince people to support the independence movement D. to tell people that elected officials routinely abused their power The two major polilitical parties in the united stated are a considered part of Under the constitution what happens when conflicts arise between state and federal government? Completa la frase con la mejor respuesta. (Complete the sentence with the best response.) Tomamos fotos con ________ . A el mensajero instantneo B la cmara digital C la direccin electrnica D la pantalla What changes occurred in the world at the end of 1980s? Which of the following rules could represent the function shown in the table? x y -1 -1 0 1 1 3A) f(x) = -2xB) f(x) = 2x - 1C) f(x) = 2x + 1 Gil evans's interest in blending jazz and rock led him to arrange works by which rock guitarist? The half life of Carbon 14 is 5500 years. How many years will pass for a 30 gram sample to reach 3.75 grams