To find out how much money will be in Tara's account after 15 years using the formula for continuously compounded interest, we can use the given formula:
\[ P(t) = 2000e^{0.05t} \]
where:
- \( P(t) \) is the amount of money in the account after \( t \) years,
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828),
- \( 0.05 \) is the annual interest rate as a decimal,
- \( t \) is the number of years.
In this case, we substitute \( t = 15 \):
\[ P(15) = 2000e^{0.05 \times 15} \]
Calculating \( 0.05 \times 15 \):
\[ 0.05 \times 15 = 0.75 \]
Now we substitute back into the equation:
\[ P(15) = 2000e^{0.75} \]
Next, we need to calculate \( e^{0.75} \):
Using a calculator:
\[ e^{0.75} \approx 2.117 \]
Finally, we multiply this by 2000:
\[ P(15) \approx 2000 \times 2.117 \approx 4234 \]
Thus,
\[ P(15) \approx 4234.00 \]
Therefore, the amount in Tara's account after 15 years will be approximately $4,234.00.
The correct answer is B $4,234.00.
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