Question

The function $f(x) = 10,000 - 1,500x$ can be used to predict the number of termites in an area $x$ days after the area has been treated. How many termites are predicted in the area after $5$ days?

Answer 1

In the given problem we have a function which predicts the number of termites left in an area after $x$ number of days and we have to calculate the number of termites left in an area after $5$ days. So, we put the value of $x$ as $5$ in the given function to calculate the number of termites left in an area after $5$ days.

Complete step by step answer:
In the given question a function $f(x) = 10,000 - 1,500x$ is used to predict the number of termites left in an area after $x$ number of days and we have to calculate the number of termites left in an area after $5$ days.
So, $x$ represents the number of days after the area has been treated
We have a function for predicting the number of termites left in an area after $x$ number of days.
So, for determining the number of termites left in an area after $5$ days. We put the value of $x = 5$ in the given function as $x$ represents the number of days after the area has been treated.
Therefore, $f(5) = 10,000 - 1,500(5)$
Simplifying the above equation. We get,
$\Rightarrow f(5) = 10,000 - 7500$
$\Rightarrow f(5) = 2500$
Hence, the number of termites left in an area after $5$ days is $2500$.

Note:
A Function defines what values need to be input in order for the calculation to run correctly.
Function also defines what is the output for the given input data. Here, the input is the number of days and the output is the number of termites left in the area after $5$ days. The number of termites left in an area depends upon the number of days. This relationship between the input value and output value is called the function rule.