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Shota invests
$1000 in a certificate of deposit that earns interest. The investment's value is multiplied by 1.02 each year.
Which expression gives the investment's value after 5 years?
Choose 1 answer:
(A)
1000+1.02^(5)
(B)
1000+(1+1.02)^(5)
(C)
1000*1.02^(5)
(D)
1000*(1+1.02)^(5)

Shota invests $\$ 1000$ in a certificate of deposit that earns interest. The investment's value is multiplied by $1$ . $02$ each year. $\newline$ Which expression gives the investment's value after $5$ years? $\newline$ Choose $1$ answer: $\newline$ (A) $1000+1.02^{5}$ $\newline$ (B) $1000+(1+1.02)^{5}$ $\newline$ (C) $1000 \cdot 1.02^{5}$ $\newline$ (D) $1000 \cdot(1+1.02)^{5}$

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Write exponential functions: word problems

Full solution

Q. Shota invests

\$ 1000

in a certificate of deposit that earns interest. The investment's value is multiplied by

1

.

02

each year.

\newline

Which expression gives the investment's value after

5

years?

\newline

Choose

1

answer:

\newline

(A)

1000+1.02^{5}

\newline

(B)

1000+(1+1.02)^{5}

\newline

(C)

1000 \cdot 1.02^{5}

\newline

(D)

1000 \cdot(1+1.02)^{5}

Understand the problem: Understand the problem. $\newline$ We need to find the value of an investment after $5$ years, where the investment increases by a factor of $1.02$ each year.
Identify the correct expression: Identify the correct expression. $\newline$ The investment is multiplied by $1.02$ each year, so we need to use an expression that represents this annual multiplication over $5$ years.
Evaluate the options: Evaluate the options. $\newline$ (A) $1000+1.02^{5}$ suggests an addition, which is incorrect for yearly multiplication. $\newline$ (B) $1000+(1+1.02)^{5}$ suggests adding $1$ to $1.02$ before raising to the power of $5$ , which is not the correct interpretation of the problem. $\newline$ (C) $1000\times1.02^{5}$ correctly represents the initial investment multiplied by $1.02$ raised to the power of $5$ , which is the number of years. $\newline$ (D) $1000\times(1+1.02)^{5}$ incorrectly suggests adding $1$ to $1.02$ before multiplying, which is not how the interest is applied.
Choose the correct expression: Choose the correct expression. $\newline$ The correct expression is (C) $1000 \times 1.02^{5}$ because it accurately represents the initial investment being multiplied by $1.02$ each year for $5$ years.

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