In 2003, the population of a town was 45000 and the population has been growing linearly by 1700 people each year. Write an equation for the population 𝑝 of 𝑡, where 𝑡 is the number of years after 2003.
Here, we have a linear equation, 𝑦 equals 𝑚𝑥 plus 𝑏. We may recognize this from graphing, where 𝑚 is the slope and 𝑏 is the 𝑦-intercept. But when thinking about this for a word problem, the 𝑦-intercept would be considered the starting point, where the slope would represent the growth.
So let’s begin plugging some things in. We are told to write an equation for the population 𝑝 of 𝑡. So instead of 𝑦, we need to use 𝑝 of 𝑡. And it says 𝑡 is the number of years after 2003. So instead of 𝑥, we will be using 𝑡.
So now let’s think about 𝑚, the slope, the growth. It says it will be growing linearly by 1700 people each year. So we have 1700 each year, so times 𝑡, plus our starting point. And the starting population was 45000. So we can either leave it like this, or we can switch the positions of the 1700 𝑡 and the 45000. It doesn’t matter. So here we would have our final answer.