A certain region had an initial rabbit population of 24, and the population is increasing at a rate of 26% each year due to a lack of natural predator

illusiia

illusiia

Answered question

2021-02-11

A certain region had an initial rabbit population of 24, and the population is increasing at a rate of 26% each year due to a lack of natural predators. Write an exponential function that models N, the number of rabbits after t years, and use it to find the expected number of rabbits after 50 years.

Answer & Explanation

Arnold Odonnell

Arnold Odonnell

Skilled2021-02-12Added 109 answers

Let the population of rabbit at time t is: N(t)
Initially the population of rabbit is given by: N0
Growth rate of the rabbit population is given by: k
Therefore the exponential model for the population of rabbit is:
N(t)=N0ekt
According to the given information:
N0=24
k=0.26
Therefore the population of rabbit at time t is:
N(t)=24e0.26t
Now expected number of rabbits after 50 years are:
N(50)=24e13
N(50)10617921
Hence expected number of rabbit after 50 years are approximately: 10,617,921

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