Question

A forest has 250 mice. The number of mice grows by 12% each year. The inequality shown can be used to calculate s, the number of years until the number of mice exceeds 3750. 250 left-parenthesis 1.12 right-parenthesis Superscript s Baseline is greater than 3750 Question In how many years will the number of mice exceed 3750?

Answer 1

Answer: The inequality given is:

250(1.12)^s > 3750

We want to solve for s, the number of years until the number of mice exceeds 3750. We can begin by dividing both sides of the inequality by 250:

(1.12)^s > 15

Next, we can take the logarithm of both sides of the inequality with base 1.12:

log₁.₁₂ [(1.12)^s] > log₁.₁₂ (15)

s > log₁.₁₂ (15)

Using a calculator, we can evaluate the right-hand side to be approximately 6.27. Therefore:

s > 6.27

Since s must be a whole number, we can round up to the nearest integer to get:

s = 7

Therefore, in 7 years the number of mice will exceed 3750.