math questions

Question

The function  f (x)= 0.4^x2-36x+1000 models the number of accidents, f (x) per Million miles driven as a function of a driver's age x in years. Find the value of and then interpret f (50)

Answer 1

In this function x = driver's age in years and f(x) = number of accidents per million miles driven.

 

f(50) just means "evaluate the function when x = 50." So, to find f(50), you plug 50 in wherever you see an x:

 

f(50) = 0.4(50)² - 36(50) + 1000

f(50) = 0.4(2500) - 1800 + 1000

f(50) = 1000 - 1800 + 1000

f(50) = -800 + 1000

f(50) = 200

 

As for what the value means... This tells us that when x = 50, f(x) = 200. In other words, a 50-year-old driver (x) has likely gotten into about 200 accidents per million miles driven (f(x)).