Q: Sam took 800 mg of Ibuprofen. Every hour, the amount decreases by 17%. How much is left after 8 hours? (Round to the nearest mg)

$800 \times (0.83)^8 \approx 263$ mg

Q: You invest $270 at 15% interest compounded weekly for 3 years. Which formula should you use to find the final amount?

$A = 270 \left(1 + \dfrac{0.15}{52}\right)^{52 \times 3}$

Q: A medication is administered at 500 mg. It decreases by 12% per hour. How much remains after 5 hours? (Round to the nearest mg)

$500 \times (0.88)^5 \approx 258$ mg

Q: A car depreciates by 10% each year. If the car is worth $30,000 now, what will it be worth in 4 years? (Round to the nearest dollar)

$30,000 \times (0.9)^4 \approx 19,683$

Question 1

Which of the following correctly simplifies the expression $2x^3 \cdot (2x^3)^4$?

Accepted Answer

$32x^{15}$

Question 2

Given the table below, which exponential function best models the data?

$x$ | $y$
0 | 3
1 | 21
2 | 147
3 | 1029

Accepted Answer

$y = 3 \cdot 7^x$

Question 3

Sam took 800 mg of Ibuprofen. Every hour, the amount decreases by 17%. How much is left after 8 hours? (Round to the nearest mg)

Accepted Answer

$800 	imes (0.83)^8 \approx 263$ mg

Question 4

Which of the following expressions is equivalent to $\dfrac{x^{11}y}{x^2y^7}$?

Accepted Answer

$x^9y^{-6}$

Question 5

A city has a population of 54,320 and grows by 3.2% per year. What will the population be in 6 years? (Round to the nearest whole number)

Question 6

You invest $270 at 15% interest compounded weekly for 3 years. Which formula should you use to find the final amount?

Accepted Answer

$A = 270 \left(1 + \dfrac{0.15}{52}ight)^{52 	imes 3}$

Question 7

Which of the following correctly simplifies $2x^2y^4 \cdot 5x^3y^3$?

Accepted Answer

$10x^5y^7$

Question 8

Suppose you are choosing between two car loans for $23,500. Bank A offers 8.5% compounded annually for 5 years. Bank B offers 1.9% compounded monthly for 3 years. Which bank will result in less total interest paid?

Accepted Answer

Bank B (1.9% compounded monthly for 3 years)

Question 9

Which of the following is the correct simplification of $\dfrac{10x^7}{2x^3}$?

Accepted Answer

$5x^4$

Question 10

Given the table below, which exponential function best models the data?

$x$ | $y$
0 | 999
1 | 333
2 | 111
3 | 37

Accepted Answer

$y = 999 \cdot (1/3)^x$

Question 11

Which of the following is the correct simplification of $x^3 \cdot x^{12} \cdot x$?

Accepted Answer

$x^{16}$

Question 12

A medication is administered at 500 mg. It decreases by 12% per hour. How much remains after 5 hours? (Round to the nearest mg)

Accepted Answer

$500 	imes (0.88)^5 \approx 258$ mg

Question 13

Which of the following is the correct simplification of $(2x^3)^4$?

Accepted Answer

$16x^{12}$

Question 14

If you invest $1,000 at 6% interest compounded monthly for 2 years, which formula gives the final amount?

Accepted Answer

$A = 1000 \left(1 + \dfrac{0.06}{12}\right)^{24}$

Question 15

Which of the following is the correct simplification of $x^2y^7 \div x^{11}y$?

Accepted Answer

$x^{-9}y^6$

Question 16

A scientist is studying bacteria that triple every 4 hours. If there are initially 200 bacteria, how many will there be after 12 hours?

Accepted Answer

$200 	imes 3^{3} = 5,400$

Question 17

Which of the following is the correct simplification of $2x^5 \cdot 7x^4$?

Accepted Answer

$14x^9$

Question 18

A car depreciates by 10% each year. If the car is worth $30,000 now, what will it be worth in 4 years? (Round to the nearest dollar)

Accepted Answer

$30,000 	imes (0.9)^4 \approx 19,683$

Question 19

Which of the following is the correct simplification of $x^2y^7 \cdot x^{11}y$?

Accepted Answer

$x^{13}y^8$

Exponential Functions and Exponent Rules Review – Step-by-Step Study Guidance

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