MATH 1101: Modeling the Fuel Consumption -- Page 3

Modeling the Flight of a Baseball

The Problem

The following table shows the distance traveled in miles,y, by a car after burning x gallons of gasoline.

x (gallons)
5

10

15

20

y (miles) 84 169 255 338

a). Make a scatterplot of the data. Could a linear function be used to model this data?
b). Find values a and b so that f(x) = ax + b models the distance traveled on x gallons of gasoline. Graph f and the data in the same viewing rectangle.
c). Interpret the slope of the graph of f.

b. In order to find a, the slope or average rate of changed must be computer. Even though this pair is not listed in the table, it is know that 0 gallons produced 0 miles, this (0,0) is also a pair for this function. Calculating the average rate of change using (0,0) and (5, 84), we get . Using other pairs of consecutive points we get:

For each pair, we get a slightly different result as this model is only approximately linear. We will use a = 17 as being an intermediate value.

The number b is easier to find. b is the y-intercept, thus we know that (0,0) is part of this function, so the y-intercept or b = 0. Thus the resulting equation is

f(x) = 17x + 0 or f(x) = 17x

To graph f and the data i the same viewing rectangle with the scatterplot, press , and enter 17x for . Note that Plot1 is still on as it is highlighted. Press GRAPH to see the results.

Note that the graph of the line y = 17x does seem to fit the data points well.

c. A slope of 17 indicates that the mileage for this car was 17 miles per gallon (mph).