At time t, the population P(t) of a certain city is increasing at a rate proportional to...

At time t, the population P(t) of a certain city is increasing at a rate proportional to the number of residents in the city at that time. In January 1990 the population of the city was 10,000, and by 1995 it had risen to 20,000.

(a) What will the population of the city be at the beginning of the year 2010?

(b) In what year will the population reach one million?

In the logistic population model (1.5.3), if P(t₁) = P₁ and P(2t₁) = P₂, then it can be shown (through some algebra performed tediously by hand, or easily on a computer algebra system) that

These formulas will be used in Problems 5–7.