Question

5. The growth rate of the world population has been increasing steadily in recent years. Someresearchers are predicting that the population will eventually stabilize. One such model is based onthe following function, where P(t) is the population in billions and t is time in years (starting at theyear 2000 when t=0). Use your graphing calculator for this question.

Answer 1

We have the next function

`P(t)=(73.2)/(6.1+5.9e^(-0.02t))`

a)

We substitute t=0 in the function

`P(0)=(73.2)/(6.1+5.9e^(-0.02(0)))=6.1`

6.1 billion in the year 2000

b)

In 2200, t=200

We substitute the value of t in the function given

`P(200)=(73.2)/(6.1+5.9e^(-0.02(200)))=11.79`

11.79 billion in the year 2200

c)

The graph of the function is

d)

The size of the world population seems to approach is 12 billion of people

ANSWER

a) 6.1 billion in the year 2000

b) 11.79 billion in the year 2200

c) see the graph above

d) 12 billion of people