Question

The average annual pay for truckers P in a certain country​ (in thousands of​ dollars) can be approximated by the following​ function, where x represents the number of years since 2000.

P=0.396x² −7.89x+74.5 ​(5≤x≤16​) Assuming the trend​ continues, find the first full year when annual pay recovered to be above ​$45 thousand.

Write the equation that can be used to find the value of x when P is exactly equal to 45.

Answer 1

To find the first full year when the annual pay recovered to be above $45 thousand, solve the equation 0.396x² -7.89x + 74.5 = 45 and find the value of x.

Step-by-step explanation:

To find the first full year when the annual pay recovered to be above $45 thousand, we need to set the equation P = 45 and solve for x.

0.396x² -7.89x + 74.5 = 45

0.396x² - 7.89x + 29.5 = 0

Using the quadratic formula, x = (-b ± √(b² - 4ac))/(2a)

Plugging in the values, we have x = (7.89 ± √((7.89)² - 4(0.396)(29.5))) / (2(0.396))

Simplifying the expression, x ≈ 6.348 or x ≈ 11.685

Since the x values represent years since 2000, the first full year when annual pay recovered to be above $45 thousand is x = 7 (2007).