Q: A savings plan requires monthly deposits of $$\100$ for 5$ years at an annual interest rate of 6$$\%$ compounded monthly. Which formula should be used to calculate the future value?

$$FV = PMT \times \frac{(1 + r)^n - 1}{r}$$

Q: A population of rabbits is currently $$500$$ and grows continuously at a rate of $$8\%$$ per year. What will the population be after $$10$$ years? (Use the continuous growth formula)

$$500 \times e$$^{0.08 \times 10}$$

Q: A savings plan has a principal of $$\1500$ and earns 5$$\%$$ annual interest compounded quarterly for 2$ years. What is the future value?

$$1500 \times (1 + \frac{0.05}{4}$$)^{8}$$

Q: A city’s population is $$80,000$$ and is expected to grow at a continuous rate of $$3\%$$ per year. Predict the population size after $$15$$ years.

$$80,000 \times e$$^{0.03 \times 15}$$

Q: A savings account earns $$7\%$$ annual interest compounded continuously. If you invest $$\5000$ for 6$ years, what is the future value?

$$5000 \times e$$^{0.07 \times 6}$$

Q: A savings plan requires you to deposit $$\100$ monthly for 5$ years at an annual interest rate of 6$$\%$$ compounded monthly. What is the total future value after 5$ years?

$$100 \times \frac{(1 + \frac{0.06}{12}$$)^{60}$$ - 1}{\frac{0.06}{12}}$$

Question 1

A hospital needs to convert a patient's medication dosage from milligrams (mg) to grams (g). If the patient is prescribed 2500 mg of a medication, how many grams is this?

Accepted Answer

$$2.5 g$$

Question 2

A savings account offers a simple interest rate of $$4\%$$ per year. If you deposit $$\2000$ for 3$ years, what is the total amount in the account at the end of 3$ years?

Accepted Answer

$$\2240$

Question 3

A chemical solution increases in concentration according to the compound interest formula. If the initial concentration is $$100$$ units and the rate is $$5\%$$ compounded annually for $$4$$ years, what is the final concentration?

Accepted Answer

$$121.55$$ units

Question 4

A biologist is studying bacteria growth, which doubles every $$6$$ hours. What is the doubling time formula for this scenario?

Accepted Answer

$$t = \frac{\ln 2}{r}$$

Question 5

A savings plan requires monthly deposits of $$\100$ for 5$ years at an annual interest rate of 6$$\%$ compounded monthly. Which formula should be used to calculate the future value?

Accepted Answer

$$FV = PMT 	imes \frac{(1 + r)^n - 1}{r}$$

Question 6

A population of rabbits is currently $$500$$ and grows continuously at a rate of $$8\%$$ per year. What will the population be after $$10$$ years? (Use the continuous growth formula)

Accepted Answer

$$500 	imes e$$^{0.08 	imes 10}$$

Question 7

A savings plan has a principal of $$\1500$ and earns 5$$\%$$ annual interest compounded quarterly for 2$ years. What is the future value?

Accepted Answer

$$1500 	imes (1 + \frac{0.05}{4}$$)^{8}$$

Question 8

A scientist wants to approximate the doubling time for a bacteria culture that grows at $$12\%$$ per hour. What is the approximate doubling time?

Accepted Answer

$$t \approx \frac{70}{12}$$ hours

Question 9

A radioactive substance decays such that half of it remains after $$5$$ years. What is the half-life fraction after $$10$$ years?

Accepted Answer

$$\frac{1}{4}$$

Question 10

A city’s population is $$80,000$$ and is expected to grow at a continuous rate of $$3\%$$ per year. Predict the population size after $$15$$ years.

Accepted Answer

$$80,000 	imes e$$^{0.03 	imes 15}$$

Question 11

A savings plan requires you to deposit $$\200$ monthly for 10$ years at an annual interest rate of 5$$\%$$ compounded monthly. What is the total number of deposits (n$) used in the savings plan formula?

Accepted Answer

$$120$$

Question 12

A medication decays in the bloodstream with a half-life of $$4$$ hours. What fraction of the medication remains after $$12$$ hours?

Accepted Answer

$$\frac{1}{8}$$

Question 13

A savings account earns $$7\%$$ annual interest compounded continuously. If you invest $$\5000$ for 6$ years, what is the future value?

Accepted Answer

$$5000 	imes e$$^{0.07 	imes 6}$$

Question 14

A scientist observes a population of bacteria that doubles every $$3$$ hours. If the initial population is $$200$$, what will the population be after $$9$$ hours?

Accepted Answer

$$200 	imes 2$$^{3}$$

Question 15

A savings plan has a principal of $$\2500$ and earns 4$$\%$$ annual interest compounded monthly for 3$ years. What is the value of n$ in the compound interest formula?

Accepted Answer

$$36$$

Question 16

A city’s population is currently $$120,000$$ and is expected to double in $$20$$ years. What is the annual growth rate $$r ($$rounded to the nearest percent)?

Accepted Answer

$$r = \frac{\ln 2}{20} \approx 0.035 or$$ $$3.5\%$$

Question 17

A savings plan requires monthly deposits of $$\150$ for 8$ years at an annual interest rate of 5$$\%$$ compounded monthly. What is the monthly interest rate r$ used in the savings plan formula?

Accepted Answer

$$r = \frac{0.05}{12}$$

Question 18

A medication has a half-life of $$6$$ hours. How long will it take for only $$12.5\% of $$the medication to remain?

Accepted Answer

$$18$$ hours

Question 19

A savings plan requires you to deposit $$\100$ monthly for 5$ years at an annual interest rate of 6$$\%$$ compounded monthly. What is the total future value after 5$ years?

Accepted Answer

$$100 	imes \frac{(1 + \frac{0.06}{12}$$)^{60}$$ - 1}{\frac{0.06}{12}}$$

Question 20

A population of bacteria triples every $$9$$ hours. What is the approximate growth rate $$r$$ per hour?

Accepted Answer

$$r = \frac{\ln 3}{9}$$

Exponential Growth, Compound Interest, and Doubling Time in College Algebra

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