An animal reserve in Arizona had 100 wild coyotes Due to dro

An animal reserve in Arizona had 100 wild coyotes. Due to drought, there were only 63 coyotes after 3 months. Assume the number of coyotes decreases (or decays) exponentially.

Determine the 3-month growth factor.

Determine the 3-month percent change. %

Determine the 1-month growth factor.

Determine the 1-month percent change.

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

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

Solution

3-month growth factor. =63/100= 0.63

3-month percent change=(1-0.63)*100 % =37 %

1-month growth factor. =(63/100)^1/3= 0.85726

1-month percent change=(1-0.85726)*100 % =14.2738 %

function, s, that determines the number of coyotes in terms of the number of months that have elapsed, t is

s=100*((63/100)^1/3)^t

s=100*(0.85726)^t

function, p , that determines the number of coyotes in terms of the number of years that have elapsed, n

p=100*((0.85726)¹²)ⁿ

p=100*(0.15752961)ⁿ