question 20 of 31\na vehicles fuel economy is affected by its speed. the data on spaller autos most popular…

question 20 of 31\na 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.\n| x | f(x) |\n| 30 | 29.4 |\n| 35 | 31.4 |\n| 40 | 33.0 |\n| 45 | 34.1 |\n| 50 | 34.8 |\n| 55 | 35.0 |\n| 60 | 34.8 |\n| 65 | 34.1 |\n| 70 | 33.0 |\n| 75 | 31.4 |\n| 80 | 29.4 |\na. 0.18 mpg/mph\nb. -5.55 mpg/mph\nc. 5.55 mpg/mph\nd. -0.18 mpg/mph
Answer
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