Question

The change in population of a town is modeled by the function p(t) = 50,000 (0.93), where p(t) is the total population

after a given number of years, t. What is the percent rate of change, and how is it interpreted in the context of the
problem?
O The percent rate of change is 93%, which means the population is decreasing by 7% per year.
O The percent rate of change is 93%, which means the population is increasing by 7% per year.
The percent rate of change is 7%, which means the population is decreasing by 7% per year.
O The percent rate of change is 7%, which means the population is increasing by 7% per year.

Answer 1

The percent rate of change for the population in the given problem is 7%. This means that the population is decreasing by 7% per year.

To understand this, let's break down the given function p(t) = 50,000 * (0.93). The number 0.93 represents the rate at which the population is changing each year. When you multiply the current population by 0.93, you get the population after one year.

In this case, multiplying 50,000 by 0.93 gives us 46,500, which represents the population after one year. This means that the population has decreased by 7% (or 7,000 people) from the initial population of 50,000.

If we continue this process, we can see that the population will continue to decrease by 7% each year. For example, after two years, the population will be 43,245 (46,500 * 0.93). And after three years, the population will be 40,286 (43,245 * 0.93), and so on.

So, the percent rate of change of 7% indicates that the population is decreasing by 7% each year.