Answer:
The answer is below
Step-by-step explanation:
The equation for a linear function is given as:
y = mx + b
where m is the slope of the function (that is the rate of change), b is the initial value of y when x is 0.
Given that the function where x represent the number of years since 1960 and y is the cost in dollar as:
[tex]f(x)=\frac{2.14}{55}x+0.31[/tex]
a) In the year 1960, that is x = 0, the cost of a gallon of gas is given as:
[tex]f(0)=\frac{2.14}{55}(0)+0.31\\\\f(0)=\$0.31[/tex]
b) From the function [tex]f(x)=\frac{2.14}{55}x+0.31[/tex], we can see that the rate of change is 2.14/55. Therefore, the cost increase each year by 4 cents per year.
