Question

A county’s population in 2019 was 103,126. In 2020, the population was 103,856. State the linear growth rate and show your work

Answer 1

Since the growth was linear, we can represent it using a linear equation, which can be expressed as below:

$y=m\cdot x+b$

Where m is the slope of the line and b is the value at which it crosses the y-axis. If we consider that 2019 is the year 0, then b will be the population at 2019. To find the value of m, we need to use the following equation:

$m=\frac{y_2-y_1}{x_2-x_1}$

Where (x1,y1) and (x2,y2) are known points. For our case, we have (2019, 103126) and (2020, 103856).

$\begin{gathered} m=\frac{103856-103126}{2020-2019} \\ m=\frac{730}{1}=730 \end{gathered}$

The linear growth rate is equal to the slope, therefore it is equal to 730.