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. years done

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. years done

Answer

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

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

Step3: Solve for t

$t=\frac{\ln(1.5)}{0.05}$ Using a calculator, $\ln(1.5)\approx0.4055$ and $\frac{0.4055}{0.05}=8.11$ Rounding to the nearest whole number, $t\approx8$

Answer:

8