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.

Part A - According to the function, what was the cost, in cents, of a gallon of gas in 1960?

Part B - According to the function, how much did the cost increase each year, rounded to the nearest whole cent?

Answer 1

The answer is below

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)=(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)=(2.14)/(55)(0)+0.31\\\\f(0)=\$0.31`

b) From the function
`f(x)=(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.