Chapter 4.6, Problem 40PE

The population of Canada P(t) (in millions) since January 1, 1900, can be approximated by

$P(t)=\frac{55.1}{1+9.6e^{-0.02515t}}$

where t is the number of years since January 1, 1900.

a. Evaluate P(0) and interpret its meaning in the context of this problem.

b. Use the function to predict the Canadian population on January 1, 2015. Round to the nearest million.

c.Use the function to predict the Canadian population on January 1, 2040.

d.Determine the year during which the Canadian population will reach 45 million.

e. What value will the term $\frac{9.6}{e^{0.02515t}}$ approach as $t\to \infty ?$

f. Determine the limiting value of P(t).