To find the amount of money in Tara's account after 15 years using the formula for continuously compounding interest, we can plug \( t = 15 \) into the equation \( P(t) = 2000 e^{0.05t} \).
The formula becomes:
\[ P(15) = 2000 e^{0.05 \times 15} \]
Calculating the exponent:
\[ 0.05 \times 15 = 0.75 \]
Now, we substitute this back into the equation:
\[ P(15) = 2000 e^{0.75} \]
Next, we need to calculate \( e^{0.75} \). Using a calculator, we find:
\[ e^{0.75} \approx 2.117 \]
Now, substituting this value into the equation gives us:
\[ P(15) = 2000 \times 2.117 \]
Calculating this product:
\[ P(15) \approx 4234 \]
Thus, the amount of money in her account after 15 years is approximately $4,234.00.
Therefore, the correct response is $4,234.00.
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