Q. 27 - Precalculus Enhanced with Graphing Utilities

Question

 Which Model? The following data represent the square footage and rents (dollars per month) for apartments in the Del Mar area of San Diego, California. 

(a) Using a graphing utility, draw a scatter diagram of the data treating square footage as the independent variable. What type of relationship appears to exist between square footage and rent? 

(b) Based on your response to part (a), find either a linear or quadratic model that describes the relation between square footage and rent.

(c) Use your model to predict the rent of an apartment in San Diego that is $850$square feet. 

Step-by-Step Solution

Answer

(a) The graph is,

(b) $R\left(x\right)=0.836x+1032.273.$

(c) The monthly rent for an apartment that has $850 sq. ft$ is $\$1743.$

Part (a) Step 1. Given information

The given table is,

We need to use the graphing utility to draw a scatter diagram of the data treating square footage as the independent variable.

Step 2. Graphing

The graph of the scatter diagram is,

From the scatter diagram we see that there is a positive linear relationship between the square footage and the monthly rent by increasing the square footage the monthly rent also increases linearly.

Part (b) Step 1. Given information

The given table is,

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

Step 2. Simplify

The linear model is of the form $y=ax+b.$ Then by entering the data in calculus we get,

$a=0.836, b=1032.273.$Let's conclude the value of $a and b$ in the linear model.

$R\left(x\right)=ax+b.$

Part (c) Step 1. Given information

The given table is,

We need to use our model to predict the rent of an apartment in San Diego that is $850 sq.ft.$

Step 2. Simplify

$R\left(x\right)=0.836x+1032.273.$

If $x=850.$

$R\left(850\right)=0.836·850+1032.273.$

            $=1742.87.$

             $\approx 1743.$