Question: Compound interest In Problem use the following information. When interest is compounded continuously, the rate of change of the amount x of the investment is proportional to the amount present. In this case, the proportionality constant is the annual interest rate r (as a decimal); that is,
dx/dt = rx
(a) If $2000 is invested at 8%, compounded continuously, find an equation for the future value of the investment as a function of time t, in years.
(b) How long will it take for the investment to double?
(c) What will be the future value of this investment after 35 years?