At the end of the zeroth year, the population is 200. At the end of the first year, the population is 200(0.96)¹ At the end of the second year, the population is 200(0.96)² We can generalise this to become at the end of the nth year as 200(0.96)ⁿ
Now, we need to know when the population will be less than 170.
So, 170 ≤ 200(0.96)ⁿ 170/200 ≤ 0.96ⁿ 17/20 ≤ 0.96ⁿ Let 17/20 = 0.96ⁿ, first. log_0.96(17/2) = n
n = ln(17/20)/ln(0.96) n will be the 4th year, as after the third year, the population reaches ≈176
