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Question

An endangered species of marsupials has a population of 462, however, following a successful breeding program the population is expected to increase by 12% each year.

1. Find an expression for the expected population size after 𝑛 years.
2. Find the expected population size after 25 years.
3. How long will it take for the population to reach 2,000? Present your answer to the nearest

month.

Answer 1

N(t) = number of animals in t years

N(t) = 462(1.12)^t

Question 2: N(25) = 462(1.12)²⁵

Question 3: 2000 = 462(1.12)^t Solve for t.