To determine the amount of money in Gabriela's account after one year using the formula for continuous compounding, we can substitute \( t = 1 \) into the formula:
\[ P(t) = 1200 e^{0.16t} \]
Substituting \( t = 1 \):
\[ P(1) = 1200 e^{0.16 \times 1} = 1200 e^{0.16} \]
Now, we need to calculate \( e^{0.16} \). Using a calculator, we find:
\[ e^{0.16} \approx 1.17351 \]
Now, multiply this value by \( 1200 \):
\[ P(1) \approx 1200 \times 1.17351 \approx 1408.21 \]
Thus, the amount of money in the account after one year is approximately $1,408.21.
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