an initial investment of $100 is now valued at $150. the annual interest rate is 5%, compounded…

an initial investment of $100 is now valued at $150. the annual interest rate is 5%, compounded continuously. the equation $100e^{0.05t}=150$ represents the situation, where $t$ is the number of years the money has been invested. about how long has the money been invested? use your calculator and round to the nearest whole number.

an initial investment of $100 is now valued at $150. the annual interest rate is 5%, compounded continuously. the equation $100e^{0.05t}=150$ represents the situation, where $t$ is the number of years the money has been invested. about how long has the money been invested? use your calculator and round to the nearest whole number.

Answer

Answer:

9

Explanation:

Step1: Isolate the exponential term

Divide both sides of $100e^{0.05t}=150$ by 100: $e^{0.05t}=\frac{150}{100} = 1.5$.

Step2: Take the natural - logarithm of both sides

$\ln(e^{0.05t})=\ln(1.5)$.

Step3: Use the property of logarithms

Since $\ln(e^{x}) = x$, we have $0.05t=\ln(1.5)$.

Step4: Solve for $t$

$t=\frac{\ln(1.5)}{0.05}$. Using a calculator, $\ln(1.5)\approx0.4055$, so $t=\frac{0.4055}{0.05}=8.11\approx9$.