Question

1. a local race for charity has taken place since 1993. using the actual speeds of the winners from 1993 through 1998, mathematicians obtained the function f(x) = 0.19x + 5.5, in which x represents the number of years after 1993 and f(x) represents the winning speed in miles per hour. in what year is the winning speed predicted to be 7.4 mph?

a. 2005
b. 2003
c. 2002
d. 2004

Explanation:

Step1: Set up the equation

We know the function is \( f(x) = 0.19x + 5.5 \) and we want to find \( x \) when \( f(x)=7.4 \). So we set up the equation:
\( 0.19x + 5.5 = 7.4 \)

Step2: Solve for x

Subtract 5.5 from both sides:
\( 0.19x = 7.4 - 5.5 \)
\( 0.19x = 1.9 \)
Then divide both sides by 0.19:
\( x=\frac{1.9}{0.19} = 10 \)

Step3: Find the year

Since \( x \) is the number of years after 1993, we add \( x = 10 \) to 1993:
\( 1993+ 10=2003 \)

Answer:

B. 2003