Iadratic Formula
Question 1,8.2.77
HW Score: $25 \%, 0.5$ of 2 points
Points: 0 of 1
A driver has something to do with his or her chance of getting into a fatal car crash. The bar graph shows the number of fatal vehicle crashes per 100 million miles driven for drivers of various age groups. For example, 25 -year-old drivers are involved in 4.1 fatal crashes per 100 million miles driven. Thus, when a group of 25 -year-old Americans have driven a total of 100 million miles, approximately 4 have been in accidents in which someone died. The number of fatal vehicle crashes per 100 million miles, $f(x)$, for drivers of age $x$ can be modeled by the following quadratic function.
\[
f(x)=0.013 x^{2}-1.19 x+28.24
\]
What age groups are expected to be involved in 2 fatal crashes per 100 mill miles driven?
-year-olds
(Round to nearest whole number. Use a comma to separate answers as nee
Get more help -
Clear all
Check a
Answer
The age groups that are expected to be involved in 2 fatal crashes per 100 million miles driven are \(\boxed{55}\) and \(\boxed{37}\) year-olds.
Step 1 ：The question is asking for the age groups that are expected to be involved in 2 fatal crashes per 100 million miles driven. This means we need to solve the equation \(f(x) = 2\) for \(x\), where \(f(x)\) is the quadratic function given in the problem.
Step 2 ：We can solve this equation using the quadratic formula. The quadratic formula is given by \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a\), \(b\), and \(c\) are the coefficients of the quadratic equation \(ax^2 + bx + c = 0\).
Step 3 ：In this case, \(a = 0.013\), \(b = -1.19\), and \(c = 28.24 - 2 = 26.24\). We can plug these values into the quadratic formula to find the solutions for \(x\).
Step 4 ：The solutions for \(x\), which represent the ages at which the number of fatal vehicle crashes per 100 million miles driven is expected to be 2, are approximately 54.51 and 37.03.
Step 5 ：However, the question asks for the ages to be rounded to the nearest whole number. Therefore, we need to round these solutions to the nearest whole number.
Step 6 ：The age groups that are expected to be involved in 2 fatal crashes per 100 million miles driven are \(\boxed{55}\) and \(\boxed{37}\) year-olds.
