Five years ago the moose population in Wells Gray Park in northern B.C. was 325. Today it is 450. What is the average annual rate of growth in the population if the moose reproduce once a year? Studies show that the park can support a population of 750 moose. How many years will it take to reach this population if the population growth continues at the same average rate?
Problems such as this can be solved using logarithms and exponentials.
Setting up the problem - translating from words to symbols:
After two years it will be P2 = P1 + P1r = 325(1+r) + 325(1+r)r = 325(1 + r)2
After five years it will be P5 = 325(1 + r)5.
and hence r = 0.067.
Therefore, the average annual rate of growth is r = 0.067 = 6.7%
Setting up the problem - translating from words to symbols:
Therefore, it will take 8 years before the poulation reaches 750.
(After 7 years it will not have reached 750, and since there are births only at one time during the year, the population will not reach 750 until 8 years later.)