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.\no 5 years\no 7 years\no 19 years\no 22 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.\no 5 years\no 7 years\no 19 years\no 22 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: Apply natural - logarithm

Take the natural logarithm of both sides: $\ln(e^{0.08t})=\ln(\frac{7}{4})$.

Step3: Use logarithm property

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

Step4: Solve for t

$t=\frac{\ln(\frac{7}{4})}{0.08}$. Calculate $\ln(\frac{7}{4})\approx0.5596$ and $\frac{0.5596}{0.08}\approx6.995\approx7$.