How long will it take for an investment to triple if it is continuously compounded at \( 9 \% \) per year? Include proper units with your solution. Round your answer to 2 decimal places.

To find out how long it will take for an investment to triple with continuous compounding, we can use the formula: \[ A = Pe^{rt} \] where: - \( A \) is the amount of money accumulated after time \( t \), - \( P \) is the principal amount (initial investment), - \( r \) is the annual interest rate (as a decimal), - \( t \) is the time in years, - \( e \) is Euler's number (approximately 2.71828). Setting \( A = 3P \) since we want the investment to triple, we can rewrite the equation as: \[ 3P = Pe^{0.09t} \] Dividing both sides by \( P \): \[ 3 = e^{0.09t} \] To solve for \( t \), we can take the natural logarithm of both sides: \[ \ln(3) = 0.09t \] Now, isolate \( t \): \[ t = \frac{\ln(3)}{0.09} \] Calculating this gives: \[ \ln(3) \approx 1.0986 \] \[ t \approx \frac{1.0986}{0.09} \approx 12.318 \] Rounding to two decimal places, it will take approximately \( 12.32 \) years for the investment to triple when continuously compounded at \( 9\% \) per year.