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

$$200 \times 3$$^{3}$$ = 5,400$$

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}$$y}{x^2$y^7$$}$?

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)

Accepted Answer

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

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

Question 7

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

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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