$10000 is deposited in an account earning 4% interest compounded continuously. Use the continuous interest formula below to determine how long it takes for the amount in the account to double. Round answer to 2 decimal places. A = P e r t_____years.

Answer:The required number of years are 7.52 years.Step-by-step explanation:Given : $10000 is deposited in an account earning 4% interest compounded continuously.To find : How long it takes for the amount in the account to double?Solution : Applying Continuous interest formula,[tex]A=Pe^{rt}[/tex]Where, P is the principal P=$10000r is the interest rate r=4%=0.04t is the time We have given, Amount in the account to doublei.e. A=2PSubstitute the value in the formula,[tex]2P=Pe^{rt}[/tex][tex]2=e^{0.04t}[/tex]Taking log both side,[tex]\log 2=\log (e^{0.04t})[/tex][tex]\log 2=0.04t\times log e[/tex][tex]t=\frac{\log 2}{0.04}[/tex][tex]t=7.52[/tex]Therefore, The required number of years are 7.52 years.