Question

The graph on the right shows the remaining life expectancy, E, in years for females of age x.Find the average rate of change between the ages of 50 and 60. Describe what the average rate of change means in this situation

Answer 1

From the graph, it can be observed that at age 50 and 60, the corresponding life expectancy is as shown below

`\begin{gathered} (50,31.8) \\ (60,22.8) \end{gathered}`

The average rate of change between the ages of 50 and 60 is

`A_{\text{rate of change}}=\frac{change\text{ in life expectancy}}{change\text{ in ages}}`
`\begin{gathered} A_{\text{rate of change}}=(22.8-31.8)/(60-50) \\ A_{\text{rate of change}}=(-9.0)/(10) \\ A_{\text{rate of change}}=-0.9 \end{gathered}`

Hence, the average rate of change between the ages of 50 and 60 is -0.9, which means that as the ages increases from 50 to 60, the life expectancy decreases at the rate of 0.9