Hello again, rom!

2. Population growth

The population of a certain city was 30,000 in 1990 and 45,000 in 2000.

The growth of this population can be described by the formula:

. . where is the population size at a particular time , and is a constant.

(a) Use this information to find the value of

In 1990

. . So we have: .

The function (so far) is: .

In 2000

. . So we have: .

Take logs: .

. . Hence: .

Therefore, the function is: .

(b) Then make a prediction of the population size for the year 2020.

In 2020

(c) Apply a suitable transformation to the population growth formula

so that you obtain an expression of the form:

We have: .

Take logs:

. .

And we have: . . . .

which is of the form: .

(d) How do and relate to the variables and ,

and the constants and in the original formula?

. .