To determine how much money Jasmine will have in her account after 15 years with continuously compounding interest, we'll use the given formula:
\[ P(t) = 1,000 e^{0.04t} \]
Where:
- \( P(t) \) is the amount in the account after \( t \) years,
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828),
- \( t \) is the time in years.
Plugging in \( t = 15 \):
\[ P(15) = 1,000 e^{0.04 \cdot 15} \]
Calculating \( 0.04 \cdot 15 \):
\[ 0.04 \cdot 15 = 0.6 \]
Now substituting this back into the formula:
\[ P(15) = 1,000 e^{0.6} \]
Next, we calculate \( e^{0.6} \). Using a calculator, we find:
\[ e^{0.6} \approx 1.82212 \]
Now substituting \( e^{0.6} \) back into the formula:
\[ P(15) = 1,000 \cdot 1.82212 \approx 1822.12 \]
Therefore, the amount of money in Jasmine's account after 15 years will be approximately:
\[ \boxed{1,822.12} \]