Question

In 1990, the population of South Carolina was approximately 3,500,000. During the next ten years, the population increased by approximately 38,500 people per year. Write a linear model (equation) that gives the population, P, of South Carolina in terms of the year, Y. Let Y = 0 correspond to 1990.

Answer 1

Explanation:

Maybe the big numbers make it confusing, so let's look at something simpler. If you start with 5 marbles and every day you add one marble to it how many will you have x days after startign the collection? Well on day 0 it's 5, on day 1 it's 6, because 5+1, on day 2 it's 5+2=7, and so on. You can write this as an equation, y = 5+x, where y is the new total and x is the number of days.

So let's move that thinking to this problem. 1990 is day 0 and you start with 3,500,000. Each year now instead of day you add 38,500. So year 0 has 3,500,000. year 1 has 3,500,000+38,500 = 3,538,500 and so on, where each year we add another 38,500. So just like in the simpler example we can rewrite this. y = 3,500,000 + 38,500x. Linear means that the x is just an x instead of something like x^2, or 1/x or something else. Just normal x.