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