Exponential Functions and Logarithmic Functions

Question

Suppose that $25,000 is invested at 4% interest compounded annually. In t years, it will grow to the amount A given by the function A(t)= 25,000 (1.04)^t. How long will it take to accumulate $80,000 in the account?

Answer 1

80000 = 25000(1.04^t

80/25 = 16/5 = 3.2 = 1.04^t

take natural logs of both sides

ln3.2= tln1.04

t = ln3.2/1.04 = time to accumulate 80K =about 29.65654411 years

= about 30 years