Question

A study found that a driver’s reaction time A(x) to audio stimuli and his or her reaction time V(x) to visual stimuli (both in milliseconds) can be modeled by

A(x) = 0.0051x² - 0.319x + 15, 16 ≤ x ≤ 70,
V(x) = 0.005x² - 0.23x + 22, 16 ≤ x ≤ 70
where x is the driver's age (in years). Write an inequality that you can use to find the x-values for which A(x) is less than V(x).

Answer 1

The required inequality is
`0.0001 x^2 - 0.089 x - 7<0`.

Explanation:

The given inequalities are

`A(x) = 0.0051x^2 - 0.319x + 15`

`V(x)= 0.005x^2 - 0.23x + 22`

where, x is the driver's age (in years), A(x) is driver’s reaction time to audio stimuli and V(x) is his or her reaction time to visual stimuli, 16 ≤ x ≤ 70.

We need to find an inequality that can be use to find the x-values for which A(x) is less than V(x).

`A(x)<V(x)`

`0.0051x^2 - 0.319x + 15< 0.005x^2 - 0.23x + 22`

`0.0051x^2 - 0.319x + 15- 0.005x^2 + 0.23x- 22<0`

Combine like terms.

`0.0001 x^2 - 0.089 x - 7<0`

where, 16 ≤ x ≤ 70.

Therefore, the required inequality is
`0.0001 x^2 - 0.089 x - 7<0`.