how long will it take for an investment to tr...

# Explanation: ## Step1: Recall continuous - compounding formula The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. We know that the investment triples, so $A = 3P$, and $r=0.08$. ## Step2: Substitute values into the formula Substitute $A = 3P$ and $r = 0.08$ into $A = Pe^{rt}$: $3P=Pe^{0.08t}$. Since $P\neq0$ (because we are making an investment), we can divide both sides of the equation by $P$ to get $3 = e^{0.08t}$. ## Step3: Take the natural logarithm of both sides Taking the natural logarithm of both sides of the equation $3 = e^{0.08t}$, we use the property $\ln(e^{x})=x$. So, $\ln(3)=\ln(e^{0.08t})$, which simplifies to $\ln(3)=0.08t$. ## Step4: Solve for $t$ We can solve for $t$ by dividing both sides of the equation $\ln(3)=0.08t$ by $0.08$. So, $t=\frac{\ln(3)}{0.08}$. We know that $\ln(3)\approx1.0986$, then $t=\frac{1.0986}{0.08}=13.7325$. # Answer: $13.7$