Money is invested at interest rate r a decimal compounded co

Money is invested at interest rate r (a decimal), compounded continuously. Express the time required for the money to quadruple, as a function of r.
Quadrupling time as a function of interest rate=

Solution

Money is invested at interest rate r (a decimal), compounded continuously

amount after time t , A=A_oe^rt, where A_o is initial amount , r is rate of interest , time is t

money to quadruple

=>4A_o=A_oe^rt

=>e^rt=4

=>rt =ln(4)

=>t =(ln4)/r

the time required for the money to quadruple t = f(r)=(ln4)/r