Animal populations are not capable of unrestricted growth because of limited hab

Question

Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model:

P(t) = d 1 + ke?ct where c, d, and k are positive constants. For a certain fish population in a small pond d = 1400, k = 13, c = 0.2, and t is measured in years. The fish were introduced into the pond at time t = 0.

(a) How many fish were originally put in the pond? 100 Correct: Your answer is correct. fish

(b) Find the population after 10, 20, and 30 years. (Round your answers to the nearest whole number.) 10 years Incorrect: Your answer is incorrect. fish 20 years fish 30 years fish

(c) Evaluate P(t) for large values of t. What value does the population approach as t ? ?? P(t) =

please show step by step

Explanation / Answer

P(t) = 1400 + 13e^-0.2t

a) plugging t = 0

P(t) = 1400 + 13e^-0.2(0)

P(t) = 1400 + 13

= 1413

there were 1413 fishes originally

b) population after 10 years

P(t) = 1400 + 13e^-0.2(10)

P(t) = 1402

population after 20 years

P(t) = 1400 + 13e^-0.2(20)

P(t) = 1400

population after 30 years

P(t) = 1400

c) for larger values of t P(t) = 1400

as you can see for t = 20 or t = 30 P(t) = 1400

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