Q31. - Algebra 1

Question

The average cost of online photos decreased from \(0.50 per print to \)0.27 per print between 2002 and 2007. Find the average rate of change in the cost. Explain what it means.

Step-by-Step Solution

Answer

The average rate of change in the cost is $-0.046\text{ dollar/year}$.

It means that per year the cost of online photos is decreasing by an amount of $\mathrm{\$}0.046$.

Step 1. Write the formula to find the average rate of change.

The Formula to find the average rate of change $\left(m\right)$ when two points are $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is:

$m=\frac{y_2-y_1}{x_2-x_1}$ 

Step 2. Find the average rate of change in the cost .

It is given that the average cost of online photos has decreased from $0.50 per print to $0.27 per print between the years 2002 and 2007.

 

Let x represents the year and represents the average cost of online photos.

Therefore, the points are $\left(2002,0.50\right)$ and $\left(2007,0.27\right)$.

 

The average rate of change $\left(m\right)$ when the two points are $\left(x_1,y_1\right)=\left(2002,0.50\right)$ and $\left(x_2,y_2\right)=\left(2007,0.27\right)$ is:

$$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{0.27-0.50}{2007-2002} \\ =\frac{-0.23}{5} \\ =-0.046 \end{gathered}$$ 

 

Therefore, the average rate of change in the cost is $-0.046\text{ dollar/year}$.

 

It means that per year the cost of online photos is decreasing by an amount of $\$0.046$.