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

Question

(a) Use the fact that the population was 250 million in 1990 (t = 0) to formulate a logistic model for the population of a particular region. (Assume the carrying capacity is 4300 million.)
P =    

(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.)
k =   

(c) Use your model to predict the population in the years 2100 and 2200. (Round your answers to the nearest whole number.)
________________ million people in 2100
________________ million people in 2200

(d) Use your model to predict the year in which the population will exceed 350 million.

Explanation / Answer

Solution:

Use P(t) = P(0)e(kt) where t is the number of years since 1990.

Population in 1990 is given as 250 million, So P(0) = 250

Population in 2000 is given as 275 million, So P(10) = 275

275 = 250e(10k)

e(10k) = 275/250 = 1.1

10k = ln(1.1)

10k = 0.0953101798

k = 0.00953102

So P(t) = 250e(0.00953102t)

Population in year 2100 ..... P(110) = 713.279335 million

Population in year 2200.....P(210) = 1.85 billion

To find the year that the population exceeds 350 million

250e(0.00953102t) 350

e(0.00953102t) 350 / 250

0.00953102t ln(1.4)

t ln(1.4)/0.00953102

t ln(1.4)/0.00953102

t 35.30285705

According to this model, the population should exceed 350 million approximately 35.3 years after 1990,

or sometime in the year 2025.

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