A conservation organization releases 40 coyotes into a preserve.After 4 years,there are 70 coyotes in the preserve.The preserve has a carrying capacity of 175.Determine the time it takes for the population to reach 140.
A)15.599 years
B)11.454 years
C)12.838 years
D)10.271 years
E)14.463 years

Question

A conservation organization releases 40 coyotes into a preserve.After 4 years,there are 70 coyotes in the preserve.The preserve has a carrying capacity of 175.Determine the time it takes for the population to reach 140. ​
A)15.599 years
B)11.454 years
C)12.838 years
D)10.271 years
E)14.463 years

Quizplus · Accepted Answer

We can use the exponential growth formula:
P(t) = P0e^(rt)

where P0 is the initial population, t is time, r is the growth rate, and P(t) is the population after time t.

We know that P0 = 40 and P(4) = 70. We want to find the time it takes for the population to reach 140, so we need to solve for t when P(t) = 140.

First, we can solve for r:
70 = 40e^(4r)
1.75 = e^(4r)
ln(1.75) = 4r
r ≈ 0.176

Now we can plug in P0, P(t), and r to solve for t:
140 = 40e^(0.176t)
ln(3.5) = 0.176t
t ≈ 12.838

Therefore, it takes about 12.838 years for the population to reach 140. The best choice is C.

A Conservation Organization Releases 40 Coyotes into a Preserve