c. What equation models the data? What are the domain and range of the equation? Explain how you determined your answers.
d. Is there a trend in the data? Does there seem to be a positive correlation, a negative correlation, or neither?
How much do you expect gas to cost in 2020? Explain.
c. To find the equation that models the data, we can analyze the pattern in the given data points. Looking at the data, we can see that the gas price is increasing linearly over time. The data points form a straight line.
Let's assume the year 1990 corresponds to x = 0. We can choose any other year as the x-coordinate and calculate the y-coordinate (gas price).
Using the first two data points (1990, $1.22) and (1995, $1.15):
Slope, m = (1.15 - 1.22) / (1995 - 1990) = -0.007
We can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
y - 1.22 = -0.007(x - 1990)
Simplifying, we get:
y = -0.007x + 14.27
This equation models the data, where x represents the year and y represents the gas price.
The domain of the equation is the range of the years (x-values) in the data set given. In this case, the domain is from 1990 (x = 0) to 2015 (x = 25).
The range of the equation is the gas prices (y-values) corresponding to the years in the data set. From the given data, the range is from $1.15 to $3.62.
d. There is a clear trend in the data. As time increases, the gas price is increasing. Therefore, there is a positive correlation, meaning that as the years go by, the gas price tends to increase.
To estimate the gas cost in 2020, we use the equation y = -0.007x + 14.27.
Plugging x = 30 (since 2020 is 30 years after 1990) into the equation:
y = -0.007(30) + 14.27
y = 0.21 + 14.27
y ≈ 14.48
We can expect the gas price to be approximately $14.48 in 2020.