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Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 10 ≤ x ≤ 15.

Given the function defined in the table below, find the average rate of change, in-example-1
User Ferhat
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1 Answer

9 votes
9 votes

The average rate of change is also known as "Slope".

The formula for calculate the slope is the following:


m=(y_2-y_1)/(x_2-x_1)

As you can notice, it can be found dividing the change in "y" by the change in "x".

In this case you have the table of a function and you need to find the rate of change over this interval:


10\le x\le15

You need to find the corresponding y-values for:


\begin{gathered} x_1=10 \\ x_2=15 \end{gathered}

As you can identify in the table, when the value of "x" is:


x=10

The value of "y" is:


y=30

And when


x=15

The value of "y" is:


y=24

Therefore, you can set up that:


\begin{gathered} y_2=24 \\ y_1=30 \\ x_2=15 \\ x_1=10 \end{gathered}

Now you can substitute values into the formula and evaluate:


m=(24-30)/(15-10)=-(6)/(5)=-1.2

The answers is:


-1.2

User DrGriff
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