Question

1. cost of gasoline (rate of change)

year: 2010, 2012, 2014, 2016, 2018
cost: $2.78, $3.62, $3.36, $2.14, $2.72
what is the average rate of change
from 2010 to 2018?
a. −$0.0075 per year
b. −$0.06 per year
c. $0.0075 per year
d. $0.06 per year

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x\) represents the year and \(y\) represents the cost of gasoline.
For the years 2010 and 2018, \(x_1 = 2010\), \(y_1=\$2.78\), \(x_2 = 2018\), \(y_2=\$2.72\).

Step2: Calculate the change in cost and change in year

First, calculate \(y_2 - y_1\): \(2.72 - 2.78=- 0.06\)
Then, calculate \(x_2 - x_1\): \(2018 - 2010 = 8\)

Step3: Compute the average rate of change

Using the formula \(\frac{y_2 - y_1}{x_2 - x_1}\), we substitute the values: \(\frac{-0.06}{8}=-0.0075\) dollars per year.

Answer:

A. \(-\$0.0075\) per year