Q44. - Algebra 2

Question

A park ranger at Blendon Woods estimates there are 6000 deer in the park. She also estimates that the population will increase by 75 deer each year thereafter. Write an equation that represents how many deer will be in the park in $\mathbf{x}$ years.

Step-by-Step Solution

Answer

The equation that represents the number of deer in $x$ years is $y=75x+6000$.

Step 1 – State the concept

The slope-intercept form of an equation of straight line is $y=mx+c$, where $m$ is the slope and $c$ is the $y$-intercept.

 Geometrically the slope represents the rate of change of $y$ and the $y$-intercept represents the value of $y$ when $x=0$.

Step 2 – List the given data

Initially there are 6000 deer in the park. The population of the deer will increase by 75 deer each year thereafter.

Step 3 – Write the equation

Let $x$ be the number of years counted from the time of the initial estimate and $y$ be the number of deer.

 It is given that at the time of initial estimate, obviously represented by    $x=0$, there are 6000 deer.

So, the value of $y$ when $x=0$ is 6000. That is, the $y$-intercept is 6000.

 Then, $c=6000$.

 It is given that the population of deer will increase by 75 deer each year.

Thus, the rate of change of $y$ is 75. So, the slope is 75.

 Then, $m=75$.

 Put $m=75$ and $c=6000$ in $y=mx+c$ to get,

 $y=75x+6000$

 So, the equation that represents the number of deer in $x$ years is $y=75x+6000$.