To determine the cost of a gallon of gas in 1960 and the rate of increase per year using the function [tex]\( f(x) = \frac{2.14}{55}x + 0.31 \)[/tex]:
1. Cost of Gas in 1960:
To find the cost of a gallon of gas in 1960, we look at [tex]\( f(x) \)[/tex] when [tex]\( x = 0 \)[/tex]. Plugging [tex]\( x = 0 \)[/tex] into the function:
[tex]\[
f(0) = \frac{2.14}{55} \cdot 0 + 0.31 = 0.31
\][/tex]
Therefore, in 1960, gas cost [tex]\(\$0.31\)[/tex] per gallon.
2. Rate of Increase per Year:
The rate of increase per year is represented by the coefficient of [tex]\( x \)[/tex] in the function. This coefficient is:
[tex]\[
\frac{2.14}{55} \approx 0.0389
\][/tex]
When rounded to the nearest cent, this translates to [tex]\(\$0.04\)[/tex] per gallon each year.
Therefore:
- In 1960, gas cost [tex]\(\$0.31\)[/tex] per gallon.
- Since 1960, the cost of gas increased at a constant rate of approximately [tex]\(\$0.04\)[/tex] per gallon.
