Q. 28 - Precalculus Enhanced with Graphing Utilities

Question

Which Model? An engineer collects the following data showing the speed s of a Toyota Camry and its average miles per gallon, $M.$

(a) Using a graphing utility, draw a scatter diagram of the data treating speed as the independent variable. What type of relationship appears to exist between speed and miles per gallon? 

(b) Based on your response to part (a), find either a linear or quadratic model that describes the relation between speed and miles per gallon.

 (c) Use your model to predict the miles per gallon for a Camry that is traveling $63$miles per hour. 

Step-by-Step Solution

Answer

(a) The graph is

(b) $M\left(S\right)=-0.0175S^2+1.935S-25.34.$

(c) Approximately $27.1$miles per gallon.

Part (a) Step 1. Given information

The given table is

We need to draw the scatter diagram of the data and determine the type of relationship to exists between square footage and rent.

Step 2. Graphing

The graph of the scatter diagram is,

This is the quadratic relationship between the variables.

Part (b) Step 1. Given information

The given table is,

We need to determine the linear or quadratic model that describes the relationship between the speed and miles per gallon.

Step 2. Quadratic relation

The function that describes the relation is given by $M\left(S\right)=-0.0175S^2+1.935S-25.34.$

Part (c) Step 1. Given information

The given table is,

We need to use our model to predict the miles per gallon for a Camry that is traveling $63$miles per gallon.

Step 2. Simplify

$M\left(S\right)=-0.0175S^2+1.935S-25.34.$

If $S=63.$

$M\left(63\right)=-0.0175{\left(63\right)}^2+1.935\times 63-25.34.$

           $\approx 27.1.$