Question

An automotive engineer studied the effect of car weight in tons on fuel efficiency, which is measured in miles per gallon (mpg). The data from two cars in the study showed that a 2 ton car had a fuel efficiency of 29 mpg and a 2.5 ton car had a fuel efficiency of 25 mpg. Find a linear model that gives the fuel efficiency E (in mpg) of a car as a function of its weight w (in tons).

Use the model to find the fuel efficiency (in mpg) of a car that weighs 3 tons.

Answer 1

To find a linear model that gives the fuel efficiency of a car as a function of its weight, we can use the given data to find the equation of the line. The linear model is E = -8w + 45. The fuel efficiency of a car that weighs 3 tons is 21 mpg.

Step-by-step explanation:

To find a linear model that gives the fuel efficiency E (in mpg) of a car as a function of its weight w (in tons), we can use the given data to find the equation of the line. We have two data points: (2, 29) and (2.5, 25).

Using the slope formula, we can find the slope of the line:

slope = (25 - 29) / (2.5 - 2) = -4 / 0.5 = -8

Now, let's use the point-slope formula to find the equation of the line:

E - 29 = -8(w - 2)

Simplifying the equation, we get:

E = -8w + 45

Thus, the linear model that relates fuel efficiency (E) to car weight (w) is E = -8w + 45.

To find the fuel efficiency of a car that weighs 3 tons, substitute w = 3 into the equation:

E = -8(3) + 45 = 21