At time t, the population P(t) of a certain city is in-creasing at a rate that is propor...

At time t, the population P(t) of a certain city is in-creasing at a rate that is proportional to the number of residents in the city at that time. In January 2000, the population of the city was 10,000 and by 2005 it had risen to 20,000.

(a) What will the population of the city be at the beginning of the year 2020?

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

In the logistic population model (1.5.3),if , then it can be shown (through some tedious algebra to derive by hand, although easy on a computer algebra system) that