Question: (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,

(a) If $2000 is invested at 8%, compounded continuously, find an equation for the 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 of this investment after 35 years?
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

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