Question

The number of fatalities due to car crashes, based on the number of miles driven, begins to climb after the driver is past age 65. Aside from declining ability as one ages, the older driver is more fragile. The number of fatalities per 100 million vehicle miles driven is approximately N(x) = 0.0336x3 − 0.118x2 + 0.215x + 0.7 (0 ≤ x ≤ 7) where x denotes the age group of drivers, with x = 0 corresponding to those aged 50-54, x = 1 corresponding to those aged 55-59, x = 2 corresponding to those aged 60-64, . . . , and x = 7 corresponding to those aged 85-89. What is the fatality rate per 100 million vehicle miles driven for an average driver in the 50-54 age group? In the 60-64 age group?†

Answer 1

The fataly rate per 100 million vehicle miles driven is approximately for average driver in the 50-54 age group is 0.7.

The fataly rate per 100 million vehicle miles driven is approximately for average driver in the 60-64 age group is 3.3268.

Explanation:

The number of fatalities per 100 million vehicle miles driven is approximately given by the following function:

`N(x) = 0.3336x^(3) - 0.118x^(2) + 0.215x + 0.7`

In which x corresponds to the age group.

What is the fatality rate per 100 million vehicle miles driven for an average driver in the 50-54 age group?

This is N(0), since
`x = 0` represents those aged 50-54.

So:

`N(x) = 0.3336x^(3) - 0.118x^(2) + 0.215x + 0.7`

`N(0) = 0.7`

The fataly rate per 100 million vehicle miles driven is approximately for average driver in the 50-54 age group is 0.7.

In the 60-64 age group?

This is N(2), since
`x = 2` represents those aged 60-64.

`N(x) = 0.3336x^(3) - 0.118x^(2) + 0.215x + 0.7`

`N(2) = 0.3336*2^(3) - 0.118*2^(2) + 0.215(2) + 0.7 = 3.3268`

The fataly rate per 100 million vehicle miles driven is approximately for average driver in the 60-64 age group is 3.3268.