Main Idea: To evaluate an exponential growth or decay function, substitute a value for the exponent variable and simplify.
Evaluate each exponential function for the given value.
Answers
In order to do this, we can just plug in 1 where it says t. It's exponential decay because the decay factor is less than one. We have:
f(t) = 2 * (1/2)^3 =
2* 1/2 * 1/2 * 1/2 =
2 * 1/8 =
2/8 =
1/4
Hope this helps!
Related Questions
Translate the algebraic expression shown below into a verbal expression
Fraction with variable x in numerator and 10 in the denominator.
A)The sum of ten and some number
B)The quotient of some number and ten
C)The product of some number and ten
D)The difference of ten and some number
Answers
The answer is:
B) The quotient of some number (x) and 10
*Remember that Fractions=Division!*
Hope this helps! :)
Answer:
it is B)The quotient of some number and ten
Step-by-step explanation:
A circle has a radius of 119.3 millimeters.
What is the circumference of this circle?
Use 3.14 for pi. Round your final answer to the nearest tenth.
Enter your answer as a decimal in the box.
mm
Answers
C = 2(3.14)(119.3)
C = 749.204
Nearest tenth would be 749.20 mm
In the United States, travel and tourism supported more than _____ jobs in the year 2010 alone.
A.5 million
B.7.5 million
C.15 million
D.20 million
will give brainliest just please answer correctly.............Im so bad at math :(
Answers
Answer:
7.5 million
Step-by-step explanation:
Plz answer both for 10 points.!!! Thx for the help.
Answers
.. A = (1/2)*b*h
23. A = (1/2)*b*h
.. A = (1/2)*x*7 . . . . substitute the given values
.. A = 3.5x . . . . . . . simplified
24. A = (1/2)*b*h
.. 84.5 = (1/2)*13*h . . . . . substitute the given values
.. 2*84.5/13 = h = 13 . . . .solve for h
The height of the triangle is 13 cm.
Andrew has $8.85 in dimes and quarters. the number of dimes he has is 3 more than twice his number of quarters. How many quarters does Andrew have?
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.. 8.55/0.45 = 19
of them.
Andrew has 19 quarters.
Estimate the sum of 9.327 + 5.72 + 4.132 to one decimal place.
Answers
In the kite ABCD m ACD=105 and m DAB=100. Find m DCB
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180 (n -2), where n is the number of sides of the polygon.
In this case, we have a 4 sided kite. So, when we plug 4 into our formula, it is re written as such:
180 (4-2)
= 180 (2)
= 360
So the sum of the interior angles of the kite must equal 360°.
We know from polygon and quadrilateral rules that kites must have one set of congruent opposite angles. To find the sum of the remaining two angles in this kite, we can determine the difference between 360° and the sum of the non-congruent opposite angles (which is given in the problem).
The solution is as follows:
105 + 100 = 205
360 - 205 = 155
Thus, 155 is the sum of the remaining two opposite angles. We know one of these has to 100°, because the kite has to have one set of congruent opposite angles. This means the measure of angle DCB is 55°.
To check, we can add these two angles together and if we are correct we should get 155.
100 + 55 = 155.
A rectangular prism has a length of 1 1/2 meters, a width of 3 meters, and a height of 5 1/2 meters. Enter the volume of the prism as a mixed number in simplest form in the box. m³
Answers
Answer:
Simplest for 36 1/5
Step-by-step explanation:
25 + 156 + 1/2 = 363/2 = 181 1/2
181÷5=36 R1
181.5=36 1/5
70 POINTS!!!!!!!!!!!!!! HELP PLEASE
1. Apply the properties of integer exponents to write equivalent numerical expressions. Show all work.
Ex. 32 • 3-5 = 3-3 =
a. 4^1 • 4^2
b. 5^3 • 5^-6
c. 32 • 31
d. 6^5 • 5^-7
2. Select two of the above expressions (one multiplication and one division) and explain how you simplified them.
Answers
5^3 * 5^-6 = 5^(3 - 6) = 5^-3 = 1/125
The third one down is rather sneaky. It's also kinda neat.
31 = 32 - 1 = 2^5 - 1
32 * 31
= 32 (2^5 - 1)
= 2^5(2^5 - 1)
= 2^10 - 2^5
= 1024 - 32
= 992
I don't see any math tricks to solve this. Use brute force.
6^5 * 5^-7 = 6^5 / 5^7 = 7776 / 17125 = 0.00953
2. Just pick a couple of questions out of the four above. The last one is a good example for division. The first one would be good for multiplication. I've explained all you need.
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
When bases are same in multiplication, add exponents.
1) a. 4^1 × 4^2
4^(1+2)
4^3
b. 5^3 × 5^-6
5^(3+-6)
5^(-3)
c. 3^2 × 3^1
3^(2+1)
3^3
d. 6^5 × 5^-7
0.0995328
2. I added the exponents. For the last one, I evaluated by calculator.
what property is 2p+(3q+2)=(2p+3q)+2
Answers
if not the associative.
Hope I helped!
A triangle in the coordinate plane has coordinates of (2,3), (-4,-5), and (-2, 4). It is reflected about the y-axis. What are its new coordinates?
A) (-2,3), (4,-5), (2,4)
B) (-2,-3), (4,5), (2,-4)
C) (2,-3), (-4,5), (-2,-4)
D) (-2,-3), (-4,-5), (-2,-4)
Answers
What is the inverse function of a(b)=12•b+9/2
Answers
To find the inverse of the function a(b) = 12b + 9/2, swap 'a' and 'b', then isolate 'b' by subtracting 9/2 and dividing by 12. This gives the inverse function as a = (b - 9/2) / 12.
Explanation:To find the inverse of a function, you need to rearrange the equation so that the independent variable 'b' becomes the dependent variable. In your function, a(b) = 12b + 9/2, first you need to solve for 'b'. Here are the steps:
Swap 'a' and 'b' to get: b = 12a + 9/2 Isolate 'b' by subtracting 9/2 from both sides: b - 9/2 = 12a Divide both sides by 12 to solve for 'a': a = (b - 9/2) / 12
So the inverse function of a(b) = 12b + 9/2 is a = (b - 9/2) / 12.
Learn more about Inverse function here:https://brainly.com/question/38141084
#SPJ11
write this ratio in another way 11/12
Answers
11 / 12
11 : 12
Those are all i can think of
On the freeway, it is unsafe to drive too slowly or too quickly. The safest driving speeds on the freeway near Allan's town were scientifically determined to be between the minimum and maximum speeds (in miles per hour) according to the equation lx-551 42. Which equation can be used to determine the maximum safe driving speed?
X-55=4.2
X-55=-4.2
X+55=4.2
X+55=-4.2
Answers
Step-by-step explanation:
the first option is the right answer
give the quotient and remainder for 693 divide by 16
Answers
You can use long division, short division, or a calculator to find the quotient to this question.
693 ÷ 16 = 43 R 11
Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Find the slope,including units, and write a sentence to interpret the slope in detail. Write an equation for the water level, y, after x days. In how many days will the water level be 26 feet? Graph the equation
Answers
Explanation of slope, equation, and days to reach a specific water level in a river.
Explanation:Slope: The slope represents the rate of change in water level per day. In this case, the slope is -0.5 feet/day, indicating that the water level is decreasing by 0.5 feet each day.
Equation: The equation for the water level after x days is y = 34 - 0.5x.
Days to reach 26 feet: To find when the water level will be 26 feet, you can solve the equation 26 = 34 - 0.5x to get x = 16 days. Therefore, it will take 16 days for the water level to reach 26 feet.
The dimensions of a parallelogram are reduced by half of its original dimensions. Determine how the perimeter of the parallelogram will be affected by the change in the dimensions of the original parallelogram..
reduced by a factor of one-fourth
reduced by a factor of one-half
increased by a factor of two
increased by a factor of four
Answers
Answer:
reduced by a factor of one-half
Step-by-step explanation:
Let one side of the parallelogram be 'a'
and the other side of the parallelogram is 'b'
Therefore the perimeter of the parallelogram given by,
P = 2 ( a + b )
Now when the dimensions are reduced to half of its original dimensions.
Then,
one side of the parallelogram be a/2
and the other side of the parallelogram is b/2
Now the new perimeter will be
P = 2 ( a/2 + b/2 )
P = 2 { (a + b)/2 }
P = a + b
Thus this clearly shows that the perimeter is reduced to one-half of the original perimeter when the dimensions are reduced by half.
Answer 3.a,3.b,3.c for 20 points
Answers
Kelly builds a dog run that is 3 feet wide and has an area of 12 square feet. The length of the dog run is feet. Kelly's brother builds another dog run that is also. 3 feet wide, but its area is double that of Kelly’s dog run. What is he length of Kelly’s brother’s dog run?
Answers
The length is 8
cougar park is shaped like a parallelogram and has an area of 1/16 sqaure mile. Its base is 3/8 mile. What is its height?
Answers
The area of parallelogram can be found using the formula:
[tex] Area = b* h [/tex]
Where b= base length and h= height.
We are given :
Area =1/16 square mile and
Base = 3/8 mile
Plugging the values in the formula to find height,
[tex] 1/16 = 3/8* h [/tex]
height = 1/6 mile
So height of parallelogram is 1/6 miles.
Please help!! Write a real-world problem for each inequality. 3x + 10 > 30
Answers
30 • (3x - 10)
Answer:
I have the same question but instead of 30 its 10.
Step-by-step explanation:
What is the area of this figure? Enter your answer in the box.
Answers
Lets break it down:
Triangle- The area of a triangle is base×height÷2
so if we plug in the numbers, the base would be 5 (the length) and the height would be 4 (the height). 5×4= 20÷2= 10.
Square- The area of a square is base×height so if we pluged in the numbers, the base is 5 (the length) and the height is 5 (the height). 5×5= 25.
10+25= 35 cm squared
Hope this helps!
The cost of going to the big playland park for a family is given by C = 15x + 50, where C represents the cost and x represents the number of family members. How many family members went if it cost them $125?
Answers
C = 15x + 50; C represents the total cost, and X represents the number of family members.
The total cost was $125, so we should substitute C with 125.
125 = 15x + 50; now, all we have to do is solve for x with basic algebra.
First, let's isolate the variable, so subtract 50 from both sides of the equation.
15x = 75; divide both sides by 15 to solve for x, the number of family members that went to the park.
15x / 15 = x
75 / 15 =5
We are left with the following solution:
x = 5
We can conclude that 5 family members went to the park.
I hope this helps!
Garrick and Zan are measuring the heights of seedling plants for science class.
Use the drop-down menus to complete the statements about the measured heights and the actual heights of the plants.
CLEAR CHECK
Because Garrick's plant is... than Zan's plant, each millimeter of error results in a ....percent error.
Garrick's measurement was ... millimeters off and Zan's was... millimeters off, so Garrick's measurement was ... % off and Zan's was
Answers
Zan's measurement was 12 mm off. (100 - 88 = 12)
Garrick's percent error was 20% (2 / 10 x 100)
Zan's percent error was 12% (12 / 100 x 100)
Answer: Garrick's plant is shorter than Zan's plant.
Each millimeter of error results in a 11.11% percent error.
Garrick's measurement was 2 millimeters off and Zan's was 12 millimeters off.
Garrick's measurement was 20% off and Zan's was 12% off.
Step-by-step explanation:
Since we have given that
In case of Garrick's plant:
Actual height of his plant = 10 mm
Measured height of his plant = 8 mm
In case of Zan's plant :
Actual height of his plant = 100 mm
Measured height of his plant = 88 mm
So, clearly Garrick's plant is shorter than Zan's plant.
Difference in actual height of plants of Garrick and Zan is
[tex]100\ mm-10\ mm=90\ mm[/tex]
similarly, difference in measured heights of plants of Garrick and Zan is
[tex]88\ mm-8\ mm\\\\=80\ mm[/tex]
Percent error will be
[tex]\frac{90-80}{90}\times 100\\\\=\frac{10}{90}\times 100\\\\=11.11\%[/tex]
So, Each millimeter of error results in a 11.11% percent error.
Error in Garrick's plant :
[tex]Actual-Measured\\\\=10-8\\\\=2\ mm[/tex]
Percent error is given by
[tex]\frac{2}{10}\times 100\\\\=20\%[/tex]
Similarly,
Error in Zan's plant ;
[tex]Actual-Measured\\\\=100-88\\\\=12\ mm[/tex]
Percent error is given by
[tex]\frac{12}{100}\times 100\\\\=12\%[/tex]
Garrick's measurement was 2 millimeters off and Zan's was 12 millimeters off.
So, Garrick's measurement was 20% off and Zan's was 12% off.
Use the formula A=bh , where A is the area, b is the base length, and h is the height of the parallelogram, to solve this problem.
Brittany is painting a mural on one of the walls in her room. The mural is in a parallelogram-shaped frame. The area of the mural is 1056 in² and the base is 32 inches.
What is the height of the mural?
Enter your answer in the box.
[___]in
Answers
1056=32xb
÷32 ÷32
33=h
The height is 33 inches.
Answer:
The height is 33 inches.
Step-by-step explanation:
A=bh
1056=32xb
÷32 ÷32
33=h
Use the commutative property of multiplication to write a related multiplication sentence 3 x 4 = 12
Answers
Rebecca left her house and walked 2 blocks east. She turned and walked 5 blocks north to get to the library. If each block is 1/4 of a mile, how far is he direct route from Rebecca’s house to the library?
Answers
Rebecca's direct route from her house to the library is approximately 1.35 miles, calculated using the Pythagorean theorem with her eastward walk of 0.5 miles and northward walk of 1.25 miles (2 blocks east and 5 blocks north, each block being 1/4 mile).
To find the direct route from Rebecca's house to the library, we can use the Pythagorean theorem since the distance forms a right triangle.
First, we calculate the distance Rebecca walked east: 2 blocks * (1/4 mile/block) = 1/2 mile.
Then, we find the distance she walked north: 5 blocks * (1/4 mile/block) = 5/4 miles.
Next, we square both distances: (1/2)^2 = 1/4 and (5/4)^2 = 25/16.
Now, we add these squares together: 1/4 + 25/16 = 16/64 + 100/64 = 116/64.
Taking the square root gives us the direct route distance: √(116/64) ≈ √1.8125 ≈ 1.35 miles.
So, the direct route from Rebecca's house to the library is approximately 1.35 miles.
1 Design your own real-world scenario in which the solution requires the Pythagorean Theorem. Use complete sentences to describe the scenario.2 Model your real-world scenario with an equation and a sketch.3 In two or more complete sentences, explain the steps necessary to solve for the missing value in your real-world scenario. Include the solution in your explanation.
Answers
3
Write a simplified polynomial expression in standard form to represent the area of the rectangle below.
A picture of a rectangle is shown with one side labeled as x-4 and another side labeled as 5x+2
A) 5x^2 + 18x - 2
B) 5x^2 + 13x + 2
C) 5x^2 - 18x - 8
D 5x^2 + 13x + 8
Answers
A= Length x width
Put values
A=(x-4)(5x+2)
Expand
A=5x²+2x-20x-8
Add like terms
A=5x²-18x-8
Answer: Option C is correct.
anwser the question quickly!