Question

The graph of f is shown. find and interpret f(45).

Answer 1

The function represents the number of accidents (f(x)) per 50 million miles driven as a function of the driver's age (x).

$f(x)=0.4x^2-36x+1000$

f(45) indicates that you have to find the value of f(x) when x=45, to do so replace the equation of the function with the value of x and solve for f(x)

$\begin{gathered} f(x)=0.4x^2-36x+1000 \\ f(45)=0.4(45)^2-36\cdot45+1000 \\ f(45)=0.4\cdot2025-1620+1000 \\ f(45)=810-1620+1000 \\ f(45)=190 \end{gathered}$

For x=45 years f(x)=190

f(45)=190; This value indicates that 45-year-old drivers had 190 accidents per 50 million miles driven.