an initial investment of $200 is now valued at $350. the annual interest rate is 8% compounded continuously…

an initial investment of $200 is now valued at $350. the annual interest rate is 8% compounded continuously. the equation $200e^{0.08t}=350$ represents the situation, where $t$ is the number of years the money has been invested. about how long has the money been invested? use a calculator and round your answer to the nearest whole number.\n5 years\n7 years\n19 years\n22 years

an initial investment of $200 is now valued at $350. the annual interest rate is 8% compounded continuously. the equation $200e^{0.08t}=350$ represents the situation, where $t$ is the number of years the money has been invested. about how long has the money been invested? use a calculator and round your answer to the nearest whole number.\n5 years\n7 years\n19 years\n22 years

Answer

Answer:

B. 7 years

Explanation:

Step1: Isolate the exponential term

Divide both sides of $200e^{0.08t}=350$ by 200: $e^{0.08t}=\frac{350}{200}=\frac{7}{4}$.

Step2: Take natural - logarithm of both sides

$\ln(e^{0.08t})=\ln(\frac{7}{4})$. Since $\ln(e^{x}) = x$, we have $0.08t=\ln(\frac{7}{4})$.

Step3: Solve for t

$t=\frac{\ln(\frac{7}{4})}{0.08}$. Using a calculator, $\ln(\frac{7}{4})\approx0.5596$ and $t=\frac{0.5596}{0.08}\approx6.995\approx7$ years.