$7450 is invested at 8.0% compounded continuously. how long will it take for the balance to reach $14900? round your answer to two decimal places, if necessary.

  8.66 years

Step-by-step explanation:

The formula for the value (A) of an investment (P) compounded continuously at annual interest rate r for t years is ...

  A = P·e^(rt)

Filling in the given values, we can solve for t:

  14900 = 7450e^(0.08t)

  2 = e^(.08t) . . . . . divide by 7450

  ln(2) = 0.08t . . . .  take the natural log

  t = ln(2)/0.08 ≈ 8.66

It will take about 8.66 years for the balance to reach $14900.