Question

question 20 of 31
a vehicles fuel economy is affected by its speed. the data on spaller autos most popular vehicle is shown in the table below where x is the speed (mph) and f(x) is the fuel economy (mpg). calculate the rate of change for the interval 40 ≤ x ≤ 50.

x	f(x)
30	29.4
35	31.4
40	33.0
45	34.1
50	34.8
55	35.0
60	34.8
65	34.1
70	33.0
75	31.4
80	29.4

a. 0.18 mpg/mph
b. -5.55 mpg/mph
c. 5.55 mpg/mph
d. -0.18 mpg/mph

Explanation:

Step1: Recall rate - of - change formula

The rate of change of a function $F(x)$ over the interval $[a,b]$ is given by $\frac{F(b)-F(a)}{b - a}$. Here, $a = 40$, $b = 50$, $F(a)=F(40)=33.0$ and $F(b)=F(50)=34.8$.

Step2: Substitute values into formula

$\frac{F(50)-F(40)}{50 - 40}=\frac{34.8 - 33.0}{10}$.

Step3: Calculate the result

$\frac{34.8 - 33.0}{10}=\frac{1.8}{10}=0.18$ mpg/mph.

Answer:

A. 0.18 mpg/mph