What is a function that represents exponential growth for this scenario

Question

Admiral Motti purchased an Imperial Frigate for 200,000 credits. The value has been increasing at the rate of 2% per year. Write a function that represents exponential growth for this scenario. How many years will it take for the frigate to be worth 300,000 credits?

Answer 1

The annual growth factor is 1.02, so after t years the Imperial Frigate is worth 200000(1.02)ᵗ.

So the value V(t)=200000(1.02)ᵗ. If V(t)=300000, increase factor is 3/2=1.5, so 1.02ᵗ=1.5.

tlog(1.02)=log(1.5), t=log(1.5)/log(1.02)=20.48 years approx.