A population of 200 animals is decreasing by a rate of. 96 per year. At this rate, in how many years will the population be less than 170?

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