Resources

Resources

Compound interest: word problems

Fred started studying how the number of branches on his tree grows over time.

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The relationship between the elapsed time

t

, in years, since Fred started studying the tree, and the number of its branches,

B_{\text {year }}(t)

, is modeled by the following function:

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B_{\text {year }}(t)=20 \cdot(2.5)^{t}

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

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Round your answer to two decimal places.

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

Enzo is studying the black bear population at a large national park.

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He finds that the relationship between the elapsed time

t

, in years, since the beginning of the study, and the black bear population

B(t)

, in the park is modeled by the following function.

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B(t)=2500 \cdot 2^{0.01 t}

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According to the model, what will the black bear population be at that national park in

25

years? Round your answer, if necessary, to the nearest whole number.

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2010

, the town of Fall River has been experiencing a growth in population.

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The relationship between the elapsed time,

t

, in years, since

2010

and the town's population,

P(t)

, is modeled by the following function.

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P(t)=36,800 \cdot 2^{\frac{t}{25}}

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According to the model, what will the population of Fall River be in

2020

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Round your answer, if necessary, to the nearest whole number.

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The present value of an investment is the amount that should be invested today at a specified interest rate in order to earn a certain amount at a future date. The amount desired is called the future value. Approximately how much should be invested today in a savings account that earns

3 \%

interest compounded annually in order to have

\$ 500

2

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1

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\$ 530

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\$ 515

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\$ 485

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\$ 471

Charlotte opened a savings account and deposited

\$800.00

as principal. The account earns

8\%

interest, compounded annually. What is the balance after

10

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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.

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Round your answer to the nearest cent.