Resources

Resources

Compound interest: word problems

\$5,000

in a savings account, and after

10

years, the balance grew to

\$8,144

. The interest is compounded annually. What is the annual interest rate? Use the formula

A = P\left(1 + \frac{r}{n}\right)^{nt}

A

is the balance (final amount),

P

is the principal (starting amount),

r

is the interest rate expressed as a decimal,

n

is the number of times per year that the interest is compounded, and

t

is the time in years. Round your answer to the nearest tenth.

\$8,000

into a savings account that has an annual interest rate of

3\%

, compounded annually. How many years will it take for your savings to increase to

\$12,000

? Use the formula

A = P\left(1 + \frac{r}{n}\right)^{nt}

A

is the balance (final amount),

P

is the principal (starting amount),

r

is the interest rate expressed as a decimal,

n

is the number of times per year that the interest is compounded, and

t

is the time in years. Round your answer to the nearest hundredth.

\$15,000

into a savings account with an annual interest rate of

5\%

, compounded annually. How long will it take for the account balance to grow to

\$25,000

? Use the formula

A = P\left(1 + \frac{r}{n}\right)^{nt}

A

is the balance (final amount),

P

is the principal (starting amount),

r

is the interest rate expressed as a decimal,

n

is the number of times per year that the interest is compounded, and

t

is the time in years. Round your answer to the nearest hundredth.

You want to know how long it will take for a retirement savings of

\$50,000

\$100,000

if it is invested at an annual interest rate of

7\%

, compounded annually. Use the formula

A = P\left(1 + \frac{r}{n}\right)^{nt}

A

is the balance (final amount),

P

is the principal (starting amount),

r

is the interest rate expressed as a decimal,

n

is the number of times per year that the interest is compounded, and

t

is the time in years. Round your answer to the nearest hundredth.

A college fund of

\$10,000

is set up with an annual interest rate of

4\%

, compounded annually. How many years will it take for the fund to reach

\$15,000

? Use the formula

A = P(1 + \frac{r}{n})^{nt}

A

is the balance (final amount),

P

is the principal (starting amount),

r

is the interest rate expressed as a decimal,

n

is the number of times per year that the interest is compounded, and

t

is the time in years. Round your answer to the nearest hundredth.

\$5,000

in a savings account that offers an annual interest rate of

6\%

, compounded annually. How long will it take for your investment to grow to

\$8,000

? Use the formula

A = P\left(1 + \frac{r}{n}\right)^{nt}

A

is the balance (final amount),

P

is the principal (starting amount),

r

is the interest rate expressed as a decimal,

n

is the number of times per year that the interest is compounded, and

t

is the time in years. Round your answer to the nearest hundredth.

\$2,000

in a savings account that offers an annual interest rate of

5\%

, compounded annually. How long will it take for your investment to grow to

\$3,000

?

\newline

Use the formula

A = P\left(1 + \frac{r}{n}\right)^{nt}

A

is the balance (final amount),

P

is the principal (starting amount),

r

is the interest rate expressed as a decimal,

n

is the number of times per year that the interest is compounded, and

t

is the time in years.

\newline

Round your answer to the nearest hundredth.

Noam had a length of

13\frac{1}{3}\,\text{cm}

of ribbon and cut

3\frac{1}{3}

equal-sized strips the full width of the ribbon.

\newline

How long is each whole strip?

\newline

\square \,\text{cm}

\triangle \mathrm{DEF}, \mathrm{m} \angle D=(x-9)^{\circ}, \mathrm{m} \angle E=(3 x-6)^{\circ}

\mathrm{m} \angle F=(10 x-15)^{\circ}

\mathrm{m} \angle E

\newline

After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly.

\newline

The relationship between the elapsed time

t

, in seconds, and the number of bacteria,

B(t)

, in the petri dish is modeled by the following function:

\newline

B(t)=8500 \cdot\left(\frac{8}{27}\right)^{\frac{t}{3}}

\newline

Complete the following sentence about the rate of change of the number of bacteria.

\newline

Round your answer to two decimal places.

\newline

Every second, the number of bacteria is multiplied by a factor of

Venera sent a chain letter to her friends, asking them to forward the letter to more friends.

\newline

The relationship between the elapsed time

t

, in months, since Venera sent the letter, and the number of people,

P(t)

, who receive the email is modeled by the following function:

\newline

P(t)=2^{3 t+7}

\newline

Complete the following sentence about the monthly rate of change in the number of people who receive the email.

\newline

Round your answer to two decimal places.

\newline

Every month, the number of people who receive the email is multiplied by a factor of

On the first day of winter, an entire field of trees starts losing its flowers. The number of locusts remaining alive in this population decreases rapidly due to the lack of flowers for them to eat.

\newline

The relationship between the elapsed time,

t

, in days, since the beginning of winter, and the total number of locusts,

N(t)

, is modeled by the following function:

\newline

N(t)=8950 \cdot(0.49)^{\frac{t}{2}}

\newline

Complete the following sentence about the daily rate of change in the locust population.

\newline

Round your answer to two decimal places.

\newline

Every day, the locust population is multiplied by a factor of

The chemical element einsteinium

253

naturally loses its mass over time.

\newline

The relationship between the elapsed time

t

, in weeks, since a sample of einsteinium was measured, and its mass,

M(t)

, in grams, is modeled by the following function:

\newline

M(t)=(0.97)^{7 t+5}

\newline

Complete the following sentence about the weekly rate of change in the mass of the sample.

\newline

Round your answer to two decimal places.

\newline

Every week, the mass of the sample is multiplied by a factor of

The amount of carbon dioxide

\left(\mathrm{CO}_{2}\right)

in the atmosphere increases rapidly as we continue to rely on fossil fuels.

\newline

The relationship between the elapsed time,

t

, in decades, since

\mathrm{CO}_{2}

levels were first measured, and the total amount of

\mathrm{CO}_{2}

in the atmosphere,

A_{\text {decade }}(t)

, in parts per million, is modeled by the following function:

\newline

A_{\text {decade }}(t)=315 \cdot(1.06)^{t}

\newline

Complete the following sentence about the yearly rate of change in the amount of

\mathrm{CO}_{2}

in the atmosphere.

\newline

Round your answer to four decimal places.

\newline

Every year, the amount of

\mathrm{CO}_{2}

in the atmosphere increases by a factor of

The number of exercises on Khan academy has increased rapidly since it began in

2006

\newline

The relationship between the elapsed time,

t

, in years, since Khan academy began, and the total number of its exercises,

E_{\text {year }}(t)

, is modeled by the following function:

\newline

E_{\text {year }}(t)=100 \cdot(1.7)^{t}

\newline

Complete the following sentence about the monthly rate of change in the number of exercises.

\newline

Round your answer to two decimal places.

\newline

Every month, the number of exercises increases by a factor of

After the last ice age began, the number of animal species in Australia changed rapidly.

\newline

The relationship between the elapsed time,

t

, in years, since the ice age began, and the total number of animal species,

S_{\text {year }}(t)

, is modeled by the following function:

\newline

S_{\text {year }}(t)=25,000,000 \cdot(0.78)^{t}

\newline

Complete the following sentence about the rate of change in the number of species in decades. Round your answer to two decimal places.

\newline

Every decade, the number of species decays by a factor of

Ju Wenjun is an ecologist who studies the change in the tiger population of Siberia over time.

\newline

The relationship between the elapsed time

t

, in years, since Ju Wenjun started studying the population, and the number of tigers,

N(t)

, is modeled by the following function:

\newline

N(t)=650 \cdot\left(\frac{16}{25}\right)^{t}

\newline

Complete the following sentence about the rate of change in the tiger population.

\newline

Round your answer to two decimal places.

\newline

The number of tigers decays by a factor of

\frac{4}{5}

\square

On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapidly increases as the trees blossom.

\newline

The relationship between the elapsed time,

t

, in days, since the beginning of spring, and the total number of locusts,

N_{\text {day }}(t)

, is modeled by the following function:

\newline

N_{\text {day }}(t)=300 \cdot(1.2)^{t}

\newline

Complete the following sentence about the weekly rate of change in the locust population.

\newline

Round your answer to two decimal places.

\newline

Every week, the number of locusts grows by a factor of

Cleopatra uploaded a funny cat video on her website, which rapidly gains views over time.

\newline

The relationship between the elapsed time,

t

, in days, since Cleopatra uploaded the video, and the total number of views,

V(t)

, is modeled by the following function:

\newline

V_{\text {day }}(t)=580 \cdot(1.17)^{t}

\newline

Complete the following sentence about the weekly rate of change in the number of views.

\newline

Round your answer to two decimal places.

\newline

Every week, the number of views grows by a factor of

The given equation shows the number of possible distinct passwords,

p

L

, where each character is selected from

n

permitted characters.

\newline

p=n^{L}

\newline

How does the number,

p

, of possible distinct passwords change if the length is increased by

3

\newline

1

\newline

p

is multiplied by

n^{3}

\newline

p

is multiplied by

3 n

\newline

p

\newline

p

is multiplied by

3

Customer acquisition cost, or CAC, is equal to the total cost of marketing and sales divided by the number of new customers. If a company spent

570

thousand dollars on a marketing campaign and got

60

000

new customers, what is the CAC in dollars per customer?

\newline

1

\newline

0

11

\newline

0

95

\newline

9

50

\newline

\mathbf{1 0 5 . 2 6}

62.4 d-210

gives the number of Indian rupees received in exchange for

d

US dollars at the local currency exchange. How many Indian rupees are received in exchange for

13

US dollars? Round the answer to the nearest whole number.

P=500(1.035)^{n}

\newline

P

, in dollars, of

\$ 500

invested in an account earning interest at a constant rate, compounded annually, after

n

years is given by the equation shown, assuming no additional investments or withdrawals are made. What is the annual interest rate on the account, in percent?

\newline

\%

symbol when entering your answer. For example, if the answer is

11.2 \%

11

2

Steven opened a savings account and deposited

\$100.00

as principal. The account earns

9\%

interest, compounded annually. What is the balance after

5

\newline

Use the formula

A = P(1 + \frac{r}{n})^{nt}

A

is the balance (final amount),

P

is the principal (starting amount),

r

is the interest rate expressed as a decimal,

n

is the number of times per year that the interest is compounded, and

t

is the time in years.

\newline

Round your answer to the nearest cent.