(a) Use the fact that the population was 250 million in 1990 (t-0) to formulate

Question

(a) Use the fact that the population was 250 million in 1990 (t-0) to formulate a logistic model for the US population. Assume the carrying capacity is 3700 million 3700 1 +13.Sekr (b) Determine the value of k in your model by using the fact that the population in 2000 was 275 million. (Round your answer to eight decimal places.) Enter a number. (c) Use your model to predict the US population in the years 2100 and 2200. (Round your answers to the nearest whole number.) P : million in 2100 million in 2200 (d) Use your model to predict the year in which the US population will exceed 350 million

Explanation / Answer

a)

Given , k= 3700

P0= 250

Find A= (3700-250)/250 =13.8

Hence , equation is

P= 3700/(1+13.8e^(-kt))

b)

given when t= 10, P=275

275 =3700/(1+13.8e^(-k*10))

1+13.8e^(-k*10) = 3700/275

13.8e^(-k*10) = (3700/275 -1)

e^(-k*10) =(3700/275 -1)/(13.8)

k=(-1/10)ln((3700/275 -1)/(13.8))

k= 0.01025829

c)

P= 3700/(1+13.8e^(-0.01025829t))

P(110) =3700/(1+13.8e^(-0.01025829*110)) = 677 million

P(210) =3700/(1+13.8e^(-0.01025829*210)) = 1423 million

d)

3700/(1+13.8e^(-0.01025829t)) >350

t= 36

hence in year 1990 +36 =2026

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