Pre-calc question, please help me with a step by step

Question

A species in danger of extinction has a population that is decreasing exponentially

Ten years ago the population was at 4000 and today only 2000 of the species are alive. Once the population drops below 500, the situation will be irreversible.

How many years from when the population was 4000 will this occur?

Answer 1

2000 = 4000(r)¹⁰

0.5 = r¹⁰

ln 0.5 = 10 ln r

-0.693 ≈ 10 ln r

-0.0693 ≈ ln r

0.933 ≈ r

500 = 4000(0.933)^t

Can you solve for t and answer?