An animal reserve in Arizona had 97 wild coyotes Due to drou

An animal reserve in Arizona had 97 wild coyotes. Due to drought, there were only 63 coyotes after 3 months. Assume the number of coyotes decreases (or decays) exponentially.

a/ Determine the 3-month growth factor.

b/ Determine the 3-month percent change.

c/ Determine the 1-month growth factor.

d/ Determine the 1-month percent change.

e/ Define a function, s, that determines the number of coyotes in terms of the number of months that have elapsed, t

f/ Define a function, p, that determines the number of coyotes in terms of the number of years that have elapsed, n.

Solution

Intial = 97 coyotes

after 3 months = 63 coy0tes

a) 3 month growth factor :

decay = (97 -63)/97 = 0.35

1 - a = 1- 0.35 = 0.65

Grwoth factor = 0.65

b) 3-month percent change. = 35%

c) 1 month growth factor

63 = 97(b)^3 where b is 1 month grwoth factor

b = (63/97)^1/3 = 0.866

1 month % change = (1- 0.866)*100 = 13.40 %

e) s(t) = 97(0.866)^t