Carlene is saving her money to buy a $500 desk. She deposits $400 into an account with an annual interest rate of 6% compounded continuously. The equation 400e^0.06t=500 represents the situation, where t is the number of years the money needs to remain in the account. About how long must Carlene wait to have enough money to buy the desk? Use a calculator and round your answer to the nearest whole number.

QUESTION POSTED AT 01/06/2020 - 04:26 PM

Answered by admin AT 01/06/2020 - 04:26 PM

We want to determine t from the equation
400e^(0.06t) = 500

Divide each side by 400.
e^(0.06t) = 1.25

Take natural log of each side.
0.06t = ln(1.25) = 0.2231
t = 3.719 yrs

Answer: 4 years (nearest whole number)
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