Question

1. using the function $v(t) = 2500(1.08)^t$, what will be the value of the investment after 15 years? round to the nearest cent.

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Explanation:

Step1: Identify the values in the function

The function is \( V(t) = 2500(1.08)^t \), where the principal amount (initial investment) is \( 2500 \), the growth factor is \( 1.08 \), and we need to find the value after \( t = 15 \) years.

Step2: Substitute \( t = 15 \) into the function

Substitute \( t = 15 \) into \( V(t) \):
\( V(15) = 2500(1.08)^{15} \)

Step3: Calculate \( (1.08)^{15} \)

First, calculate \( (1.08)^{15} \). Using a calculator, \( (1.08)^{15} \approx 3.172169114 \)

Step4: Multiply by the principal amount

Multiply this result by \( 2500 \):
\( V(15) = 2500 \times 3.172169114 \approx 7930.422785 \)

Step5: Round to the nearest cent

Rounding \( 7930.422785 \) to the nearest cent (two decimal places) gives \( 7930.42 \)

Answer:

\( \$7930.42 \)