Question

o05 AC)= 1,000e0 4. Ellen put $1,000 into a new savings account that paid 5% interest per year, compounded continuously. She made no deposits to or withdrawals from the account, and the amount, A(), in dollars, in the account t years from the time she opened the account is given by the function above. At this rate, how many years from the time she opened the account did the value of the account increase by 50 percent? (Round your answer to the nearest tenth of a year. Type your answer into the box below.)

Answer 1

Given A(t) = 1000e^(0.05t)

the time for which investment increases 50%

1.5*1000 = 1000 * e^(0.05t)

ln(1.5) = 0.05t

t = 8.109 years