Question

The function f(x)=2.14/55x + 0.31 can be used to determine the cost, in dollars, of a gallon of gas x years since 1960.

Answer 1

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:

$f(x)=\frac{2.14}{55}x+0.31$

a) In the year 1960, that is x = 0, the cost of a gallon of gas is given as:

$f(0)=\frac{2.14}{55}(0)+0.31\\\\f(0)=\ 0.31$

b) From the function $f(x)=\frac{2.14}{55}x+0.31$, we can see that the rate of change is 2.14/55. Therefore, the cost increase each year by 4 cents per year.