Question

The mayor of a city records the population each year since 1980. He models the data as P(t)=16.8(0.94)^t. Where P represents the city’s population, in thousands of people and t represents the number of years since 1980

Select each true statement based on the population model.
A. The population has been increased since 1980
B. The population has changed by 94% each year since 1980
C. The population has changed by 6% each year since 1980
D. The population was 16,800 people in 1980
E. The population was 9,400 people in 1980
F. The population has been decreased since 1980

Answer 1

C, D, F are correct.

Explanation:

If we look at the equation:

`P(t)=16.8(0.94)^t`

Is molded after this equation:

`Population_(final)=Population_(initial)(1+r)^t`

Where 1 represents 100%, r is the rate in decimals and t is time.

So this means that the initial population is 16.8 thousand or in other words 16,800 people. The rate is 1-r, so the rate that the population is decreasing is 0.06 i.e. 6% (because 1-0.06=0.94).