The population of Arizona was 5.1 million in 2000 and 7.7 million in 2008. If the population grew linearly, which one of the following models the population as a function of time (in years since 2000)?

Question

Quizplus · Accepted Answer

We know that the population grew from 5.1 million in 2000 to 7.7 million in 2008. That means that the population grew by 2.6 million over the course of 8 years. To find the yearly growth rate, we can divide the total growth by the number of years between the two data points:

2.6 million / 8 = 0.325 million per year

So, we can model the population as a linear function with a slope of 0.325 million per year. Let time be represented by t, where t = 0 corresponds to the year 2000.

The initial population in 2000 is 5.1 million, so our equation for the population as a function of time is:

P(t) = 0.325t + 5.1

To check if this model is correct, we can substitute t = 8 (for the year 2008) and see if we get 7.7 million:

P(8) = 0.325(8) + 5.1 = 7.7

So, our final equation for the population of Arizona as a function of time (in years since 2000) is:

P(t) = 0.325t + 5.1

This matches choice B.

The Population of Arizona Was 5