Suppose that $2500 is invested at interest rate k, compounded continuously, and grows to $4000.00
after 5 years.
a. What is the interest rate?
b. Find the exponential growth function.
c. What will the balance be after 10 years?
d. After how long will the $2500 have doubled?

Question

Suppose that $2500 is invested at interest rate k, compounded continuously, and grows to $4000.00
after 5 years.
a. What is the interest rate?
b. Find the exponential growth function.
c. What will the balance be after 10 years?
d. After how long will the $2500 have doubled?

kropot72 · Answer

$$A=Pe ^{rt}$$
where, P = principal amount (initial investment)
r = annual interest rate (as a decimal)
t = number of years
A = amount after time t
 The question is somewhat confusing in denoting k as the interest rate.
The answer to part a is found by solving the following equation for r and converting the result to a percentage.
$$4000=2500e ^{5r}$$