Plzz help (Calculus).. quick help :) Urgent

Question

You put D0 dollars into your savings account in a bank that offers a fixed annual interest rate. If the interest is compounded continuously, one can derive that at a later time, in year t>0, the total amount in your savings account will be D(t)=D0e^rt.

(a)Assuming interest is compounded continuously as mentioned above, how many years will it take for your savings to double?

(b) Show that after t=lnT=loge T years, the total savings in your account will be D0T^r dollars.

Answer 1

D(t) = D₀e^rt

You double your money when 2D_o = D₀e^rt.

2 = e^rt So, ln2 = ln(e^rt) = rt. Therefore, t = ln2 / r.

When t = lnT, D(t) = D₀e^rlnT = D₀e^{ln(T^r)} = D₀ T^r