A lab worker monitors the growth of a bacteria colony starting at 9:00 a.m. At that time, there are 100 bacteria. According to the exponential function f(x) = 100(4)x, the bacteria quadruple every hour. Which equation could you use to determine the number of bacteria in the colony after 6 hours?

Answers

Answer 1

We know that the exponential growth of the Bacteria's population is model by the function [tex]f(x)=100(4)^x[/tex], so to find the number of bacteria after 6 hours, we just need to evaluate our function at [tex]x=6[/tex]. In other words, we are going to replace [tex]x[/tex] with 6 in our function:
[tex]f(x)=100(4)^x[/tex]
[tex]f(6)=100(4)^6[/tex]
[tex]f(6)=409600[/tex]

We can conclude that the we should use the equation: [tex]f(6)=100(4)^6[/tex] to find the number of bacteria in the colony after 6 hours. Evaluating the function we get that the number is 409,600.

Answer 2

The equation to determine the number of bacteria in the colony after 6 hours is [tex]f(x) = 100(4)^x[/tex] and after 6 hours, there will be 409,600 bacteria in the colony.

To find the number of bacteria after 6 hours, one would substitute x with 6 in the exponential function [tex]f(x) = 100(4)^x[/tex].

This function models the growth of the bacteria colony, where the initial number of bacteria is 100 and they quadruple every hour.

The variable x represents the number of hours that have passed since the initial measurement at 9:00 a.m.

By substituting x = 6 into the function, we get:

[tex]f(6) = 100(4)^6[/tex]

Now, calculate the value of [tex](4)^6[/tex]:

[tex](4)^6 = 4 \times 4 \times 4 \times 4 \times 4 \times 4 = 4096[/tex]

Then, multiply this by the initial number of bacteria, which is 100:

f(6) = 100 [tex]\times[/tex] 4096

Finally, calculate the total number of bacteria after 6 hours:

f(6) = 409600

Related Questions

Two campers leave their campsite at point A to go on a hike. Camper one heads east for 2 miles, then heads north 1 mile to point B. Camper two heads north for 4 miles, then east for 3 miles to point C. Referencing the triangle formed by A, B, and C, m
A.
27°
B.
36°
C.
45°
D.
53°

Answers

Answer:

its not C. It's A. 27

I just did it with my math teacher

What are angle a and the 60-degree angle to one another?

Answers

The answer to this is vertical angles i just got finished taking it

Richard can read 1/4 of a book in 3/5 of an hour. At this rate, how much can Richard read in one hour

Answers

3/5 hour ⇒ 1/4 of the book

Find 1/5 hour:
1/5 hour ⇒ 1/4 ÷ 3 = 1/4 x 1/3 = 1/12 of the book

Find 5/5 (1 hour):
5/5 hour ⇒ 1/12 x 5 = 5/12 of the book

Answer: 5/12 of the book

For a propular Broadway musical the theater box office sold 356 tickets at $80 apiece,275 tickets for $60 apiece and 369 tickes $45 apiece. How much money did the box office take in

Answers

The first step to solving this equation would be to how much they made for every apiece. To do this we must multiply the cost of the $80 apiece by how much they sold, as well multiplying the $45 apiece by how many they sold. And also the $60 apiece by the how many they sold.

$80 apiece × 356 tickets = ?

$60 apiece × 275 tickets = ?

$45 apiece × 369 tickets = ?

Now we must solve our equations.

$80 apiece × 356 tickets = $28,480

$60 apiece × 275 tickets = $16,500

$45 apiece × 369 tickets = $16,605

The next step would be to add up all the total costs of each apiece.

$28,480 + $16,500 + $16,605 = $61,585

So our answer is...

The box office took in a total of $61,585

If Jane has 3 3/4 dozen boxes of envelopes, and she ordered 11 1/2 dozen more, how many dozen boxes will she have in all?

Answers

Final answer:

Jane has a total of 61/4 dozen boxes of envelopes after adding the original 3 3/4 dozen with the additional 11 1/2 dozen she ordered.

Explanation:

If Jane has 3 3/4 dozen boxes of envelopes, and she orders 11 1/2 dozen more, we must add these two amounts together to find out how many dozen boxes she will have in all. First, we convert 3 3/4 to an improper fraction: 3 x 4 + 3 = 12 + 3 = 15, so 3 3/4 dozen becomes 15/4 dozen. Similarly, we convert 11 1/2 to an improper fraction: 11 x 2 + 1 = 22 + 1 = 23, so 11 1/2 dozen becomes 23/2 dozen.

Next, we add the two amounts of dozens of boxes together:

(15/4) dozen + (23/2) dozen

To add these fractions, we need a common denominator, which is 4, so we convert 23/2 to 46/4.

(15/4) dozen + (46/4) dozen = (61/4) dozen

So, in total, Jane will have (61/4) dozen boxes of envelopes.

Someone please help me?

Answers

(AE + ED) *AE = (CB+ AB) *AB

(4 + ED) * 4 = (4+5) *5

(4 + ED) * 4 = 45

4ED +16 = 45

4ED = 29
ED = 29/4 = 7.25

AD = AE + ED

AD = 4 + 7.25

AD = 11.25

Answer is A

Suppose that a small town has seven burger shops whose respective shares of the local hamburger market are (as percent- ages of all hamburgers sold): 23 percent, 22 percent, 18 percent, 12 percent, 11 percent, 8 percent, and 6 percent. what is the four-firm concentration ratio of the hamburger industry in this town

Answers

SADNADDDDDDDDDDDDDSLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLDNNNNNNNNNNNNNNNNNNNNNNNNNNNNEL

The volumes of two spheres are in a ratio of 1:8. what is the ratio of their radii?

Answers

we know that

volume of a sphere=(4/3)*pi*r³

let
A-----> smaller sphere
B-----> larger sphere

VA=(4/3)*pi*rA³
VB=(4/3)*pi*rB³
VA/VB=1/8--------> (1/8)=[(4/3)*pi*rA³]/[(4/3)*pi*rB³]

(1/8)=[rA³]/[rB³]-----> (1/8)=[rA/rB]³-----> rA/rB=∛(1/8)----> rA/rB=1/2

the answer is
the ratio of their radii is (1/2)

Jenna uses 18 inches if ribbon for each box she wraps how many yds of ribbon does she need to wrap 4 boxes

Answers

She needs 2 yards of ribbon to wrap 4 boxes.

if she uses 18 inches for each box then for 4 boxes she will use 18+18+18+18 or 18×4=72 inches.
since 1 yard is 36 inches she will need 72/36=2 yards.

if you like my answer please rate as brainliest! thx

What is the value of r?

Answers

good day ^-^ ///////////////

Answer:R = 4

Step-by-step explanation:

Please Help! 16 points!

The equation 1.6x − 2.2 = 1.4x can be transformed to form which of the following expressions?

Select one:

a. 3.0x = 2.2

b. 0.2x = −2.2

c. 3.0x = −2.2

d. 0.2x = 2.2

Answers

The answer is D, 0.2x = -2.2

You must simplify the equation using SADMEP, the reverse order of operations in which subtraction is the first step. Your goal is to isolate the variable.

First, subtract 1.6 from each side:

1.6x - 2.2 = 1.4x
-1.6x -1.6x
------ --------

This will get you to 0x - 2.2 = -0.2x, or -2.2 = -0.2x

This is equivalent to 2.2 = 0.2x

So, the equation can be simplified to 0.2x = 2.2

Hope this helps, let me know if you need anything else! :)

Answer:

Step-by-step explanation:

Using differentiation from first principles, prove that the gradient of the line y=mx + c is m

Answers

[tex] \frac{dy}{dx} = m[/tex]
because when you differentiate, only the constant of the x remains (which is m in this case), and c being another constant independent of x, is 0 when differentiated. hence, since dy/dx is the gradient of the line, m is therefore the gradient

15 min left! Anyone know this geometry question?

Answers

Option B is your answer. Those two angles are alternate interior angles.

what does –x2 – 6x – 8 look like on a graph
The 2 is a power

Answers

Does this answer your question?

The equation -x^2 - 6x - 8 looks like this when graphed.

I hope this helps!

pls help with this pre-calc question on vectors!!

Answers

The answer is the option C, which is:

C. √29

The explanation of this exercise is:

To solve this problem you must apply the proccedure shown below:

1- You have that:

W (-2,8,-3) and X(1,4,-1)

2- Therefore, you can calculate the magnitude as below:

|WX|=√[(1-(-2)]²+(4-8)²+[(-1-(-3)]²)
|WX|=√29

a ice cream shop offers 5 different flavors of ice cream and 12 different toppings how many choices are possible for a single serving of ice cream with one topping

a. 18
b. 22
c. 46
d. 60
PLZ HELP

Answers

60 because 5 times 12 equals 60

Answer:

D)60

Step-by-step explanation:

All you do is multiply 5 by 12.

5x12=60

Your brother and sister took turns driving on a 580 mile trip that took 10 hours to complete. your brother drove at a constant speed of 55 miles per hour and your sister drove at a constant speed of 60 miles per hour. how long did each person drive.

Answers

let the time the boy drove be x and that the girl drove be y:
x+y=10
thus
x=10-y........i

distance=speed*time
the distance each one drove will be:
55x+60y=580....ii
substituting i in ii we get:
55(10-y)+60y=580
550-55y+60y=580
5y=30
y=6 hours
thus
x=10-6=4 hours
hence the boy drove for 4 hours and the girl for 4 hours

Using a system of equations, it is found that the brother drove for 4 hours and the sister drove for 6 hours on their 580-mile, 10-hour trip.

To solve this problem, let's assign variables to the unknown quantities. Let x be the number of hours your brother drove and y be the number of hours your sister drove. We know they drove for a combined total of 10 hours and covered 580 miles together. This gives us two equations:

Equation 1 (Total Time): x + y = 10Equation 2 (Total Distance): 55x + 60y = 580

Since there are two equations with two unknowns, we can solve for x and y by using substitution or elimination method. Let's use the substitution method:

Solve Equation 1 for y: y = 10 - xSubstitute y into Equation 2: 55x + 60(10 - x) = 580Simplify and solve for x: 55x + 600 - 60x = 580, which gives us -5x = -20, so x = 4.Now substitute x back into Equation 1 to find y: y = 10 - 4, so y = 6.

Therefore, your brother drove for 4 hours, and your sister drove for 6 hours.

98 POINTS PLEASE HELP
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Determine the standard form of the equation for the circle

With center (h,k)=(-5,1/2) and radius r=1

A) (x-5)^2 + (y + 1/2)^2 = 1

B) (x-5) + (y - 1/2) = 1

C) (x+5)^2 + (y - 1/2)^2 = 1

D) (x+5)^5 + (y- 1/2)^2 = 105/2

Answers

The standard form of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex]. We will fill in our h, k and r accordingly. [tex](x-(-5))^2+(y- \frac{1}{2})^2=1^2 [/tex] which simplifies down to [tex](x+5)^2+(y- \frac{1}{2})^2=1 [/tex] choice C. There you go!

Hello!

I believe the answer is C) (x+5)^2 + (y - 1/2)^2 = 1.

I hope it helps!

Leah pays $40 a month for cable TV, plus $4 for each movie she orders on pay-per-view. Which equation gives Leah’s total monthly cable bill as a function of the number of pay-per-view movies m that she orders?

Answers

m = movies
b = bill

b = 4m + 40

I hope this helps

An equation which gives Leah’s total monthly cable bill is b=4m+40.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Leah pays $40 a month for cable TV, plus $4 for each movie she orders on pay-per-view.

Let the number of pay-per-view movies she orders be m and the total monthly cable bill be b.

Now, b=4m+40

Therefore, an equation which gives Leah’s total monthly cable bill is b=4m+40.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ5

Aaron is rolling the fair number cubes. What is the probability both cubes show a 5

Answers

The probability of two dice being the same particular number is 1/6 x 1/6 = 1/36. This is not the same as saying that both dice are the same number. There are six different possible numbers, so that would be 6/36 or 1/6.

Brainly please

Evaluate the following in polar and standard forms. Select all answers that apply. [3(cos(27°) isin(27°))]^5

Answers

Using De Moivre's formula

if z = a ( cos x + i sin x ) ⇒⇒⇒ ∴ z^n = a^n ( cos nx + i sin nx)

Part (1)
∴ [ 3 (cos 27° + i sin 27°) ]⁵ = (3⁵) ( cos 5*27° + i sin 5*27°)
= 243 ( cos 135° + i sin 135°) ⇒⇒⇒⇒ Polar form
=================================
Part (2)

The angle 135° in the second quadrant ⇒ sin is (+) and cos is (-)
and its reference angle = 180° - 135° = 45°
sin 45° = cos 45°= 1/√2 = (√2)/2
∴ sin 135° = (√2)/2    and cos 135° = -(√2)/2
∴ 243 ( cos 135° + i sin 135°) = 243 [ -(√2)/2 + i (√2)/2 ]

= - 243(√2)/2 + 243 (√2)/2 i ⇒⇒⇒⇒ standard form
===========================================
The correct answers are options (1) and (3)

option (1) ⇒⇒⇒ 243 ( cos 135° + i sin 135°) ⇒⇒⇒⇒ Polar form
option (3) ⇒⇒⇒ - 243(√2)/2 + 243 (√2)/2 i     ⇒⇒⇒⇒ standard form

A gazebo is located in the center of a large circular lawn with a diameter of 300 feet. straight paths extend from the gazebo to a sidewalk around the lawn. if two of the paths form a 45 angle, how far would you have to travel around the sidewalk to get from one path to the other? Round your answer to the nearest foot

Answers

1.To solve this problem you must apply the formula for calculate the arc length, which is:
arc length=2πr(central angle/360)
r=300 feet/2
r=150 feet
central angle=45°
2. When you substitute the values, you obtain
arclength=118 feet
The answer is: 118 feet

Answer: 118

Step-by-step explanation:

1.To solve this problem you must apply the formula for calculate the arc length, which is:

arc length=2πr(central angle/360)

r=300 feet/2

r=150 feet

central angle=45°

2. When you substitute the values, you obtain

arclength=118

Question 2 (Matching Worth 4 points)

Match the sequence (term) with the correct type of sequence (definition).

Match Term Definition

128, 32, 8, 2, … A) Geometric, common ratio is 0.25

1, 3, 9, 27, … B) Geometric, common ratio is 3

5, 10, 15, 20, … C) Arithmetic, common difference is −3

20, 17, 14, 11, … D) Arithmetic, common difference is 5

Answers

Switch c, and d.
Which makes it so that the common difference between 5, 10, 15, 20 is 5.
Then the difference between 20, 17, 14, 11 ... is -3.
Other than that your correct

1.
A. 3.75
B. 1.5
C. 3
D. 4.5

2.
A. 30
B. 16
C. 8
D. 15

Answers

b: 3.75 since it is half of the segment that measures 7.5, this is proven because the line in the middle is a bisector of the top and bottom line indication that both half measure the same; 3.75

2) 15 not sure why

0.6704 repeating as a fraction?

Answers

Suppose [tex]x=0.67046704\ldots[/tex].

Then [tex]10^4x=6704.67046704\ldots[/tex], and we have

[tex]10^4x-x=9999x=6704[/tex]

which means

[tex]x=\dfrac{6704}{9999}[/tex]

Find the volume of the square pyramid to the nearest cubic unit. edge 10 ft; height 11 ft 1,467 ft3 1,100 ft3 550 ft3 367 ft3

Answers

we know that
[volume of square pyramid]=(1/3)*b²*h
where
b is the length side of the square base-----> 10 ft
h is the height-----> 11 ft
[volume of square pyramid]=(1/3)*10²*11----> 366.67 ft³-----> 367 ft³

the answer is
367 ft³

A pet store has two tanks of tropical fish. The first tank contains 7 blue fish and 3 yellow fish and the second tank contains 10 blue fish and 8 yellow fish. If Keisha randomly purchases a fish from each tank, what is the probability that both fish will be blue? A. 1/70 B. 17/180 C. 7/18 D. 17/28

Answers

In the first tank we have 7 blue fish and 3 yellow fish, so total number of fishes in tank 1 = 10

The probability of picking a blue fish in tank 1 = number of blue fishes/ total number of fishes = 7/10

The second tank has 10 blue fish and 8 yellow fish, so the total number of fishes in tank 2 = 18

The probability of picking a blue fish in tank 2 = number of blue fishes/ total number of fishes = 10/18

The probability that both fish will be blue = 7/10 * 10/18 = 70/180 = 7/18 (Option C)

Does anyone know how to find x?

Answers

Hello!

We can solve this using trigonometric functions. We will be referring to the 70 degree angle. We need to solve for the hypotenuse. We have the length of the opposite side and need to find the hypotenuse. Therefore, we use the sine.

sin70=12/x

Since we cannot immediately solve for x, we will simplify this equation. We multiply both sides by x.

x(sin70)=12

Divide both sides by sin70.

x=12/sin70

Now we solve this equation.

12/sin70≈15.51

Therefore, x=15.51 cm.

I hope this helps!

x=15.51cm

70+90+x=180

Anybody know the answer to this question?

Answers

I'm pretty sure it is 17.5

Help me with this algebra problem. Thank you :)

Answers

To solve this problem you must apply the proccedure shown below:

1. You must make a system of equations, as below:

2. Let's call:

x: the number of first class tickets bought.
y: the number of coach tickets bought.

3. Then, you have:

x+y=7 (First equation)
970x+370y=3790 (Second equation)

x=7-y

4. By substitution, you have:

970x+370y=3790
970(7-y)+370=3790
y=5

x=7-y
x=7-5
x=2

Therefore, the answer is:

- Number of first class tickets bought=2

- Number of coach tickets bought=5

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