Hello, eh501!

Since January 1980, the population of the city of Brownville has grown

according to the mathematical model:

where is the number of years since January 1980.

(a) Explain what the numbers 720,500 and 1.022 represent in this model.

Let and we have: .

That is, when time is 0, the population was 720,500.

Therefore, 720,500 is the initial population of the city (in 1980).

The population is growing by a factor of 1.022 each year.

This means that the population is growing by 2.2% annually.

(b) If this trend continues, use this model to predict the year

during which the population of Brownville will reach 1,548,800.

Then question is: for what will ?

We have: .

Take logs: .

Hence: .

Therefore, the population will reach 1,548,800 during the 35th year (2015).