Last confusing problem for the day for points?

Question

Often environmentalists capture an endangered species and transport the species to a controlled environment where the species can produce offspring and regenerate its population. Suppose that six American bald eagles are captured, transported to Montana, and set free. Based on experience, the environmentalists expect the population to grow according to the model
P(t)= 500/ 1+83.33e^-0.162t
where t is measured in years.
a) determine the carrying capacity of the environment
b)what is the growth rate of the bald eagle?
c)what is the population after 3 years?
D)when will the population be 300 eagles?
e)How long does it take for the population to reach one-hhalf of the carrying capacity?

Answer 1

a-carrying capacity is the population at oo, which is 500

b-You need to find dP/ dt

c- set t = 3 and solve for P

d-Set P = 300 and solve for t

e- set P = 250 and solve for t

Answer 2

1

Answer 3

a) carrying capacity is lim(t→∞) P(t) = 500 (as t→∞, e^-kt→0 so P = 500/1)

b) dP/dt = 1.3 according to ti-89

c) P(3) = 500/[1 + 500/6 e^-0.486] = 9.568

d) 300 = 500/[1 + 500/6 e^-0.162t]
3/5 = 1/[1 + 500/6 e^-0.162t]
5/3 = 1 + 500/6 e^-0.162t
2/3 = 500/6 e^-0.162t
1/125 = 0.008 = e^-0.162t
ln 0.008 = -.162t
t = ln 0.008 / -.162 = 29.8 y

e) 250 = 500/[1 + 500/6 e^-0.162t]
1/2 = 1/[1 + 500/6 e^-0.162t]
2 = 1 + 500/6 e^-0.162t
1 = 500/6 e^-0.162t
6/500 = 0.012 = e^-0.162t
ln 0.012 / -0.162 = 27.3 y

Answer 4

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Answer 5

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Answer 6

Bald eagles are fishing birds and would not do well on the plains of Montana

Answer 7

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