To find the investment amount after 9 years using the continuous change function \( A(t) = Pe^{rt} \), we need to identify the values of \( P \) (the initial investment), \( r \) (the interest rate), and \( t \) (the time in years).
Given:
- \( P = 10,500 \)
- \( r = 0.0375 \) (3.75% expressed as a decimal)
- \( t = 9 \)
Now, plug in the values into the formula:
\[ A(t) = 10,500 \times e^{(0.0375 \times 9)} \]
Calculating \( 0.0375 \times 9 \):
\[ 0.0375 \times 9 = 0.3375 \]
Now we find \( e^{0.3375} \):
\[ e^{0.3375} \approx 1.40286 \]
Now, substitute this back into the formula for \( A(t) \):
\[ A(t) = 10,500 \times 1.40286 \approx 14,715.03 \]
Rounding to two decimal places, the final amount is approximately:
\[ A(t) \approx 14,715.12 \]
So, the correct response is:
$14,715.12
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