1. ## Exponential Word Problem

An investment pays 8% interest, compounded annually.

a) write an equation that expresses the amount, A, of the investment as a function of time, t, in years.

b) determine how long it will take for this investment to double in value and then to triple in value.

c) determine the percent increase in value of the account after 5 years and then after 10 years.

d) explain why the answers to parts b and c do not depend on the amount of the initial principal.

I need help with part c and d please and thank you.

for a and b my answers are:
a) A(t)=A_o(1.08)^t
b) double in value in 9 yrs and triple in value in 14 years

for part c) consider the return after 5 years.

$\displaystyle A = A_0\times(1.08)^5$

$\displaystyle A = A_0\times1.469$

This means not matter what the initial amount invested was the return will always be 1.469 times larger. Now look at turning this into a %.

the same can be said for comparing amounts after tens years, give it a shot, this should also be a major hint for part d)

$\displaystyle A = A_0\times(1.08)^{10}$ ....