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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