Chapter 1.3, Problem 92E

To determine

To calculate:

Model for cost $C$ of the package as a function of weight $x$ and graph of function.

Answer to Problem 92E

Cost of $C$ of package as a function of weight $x$ can be given by model,

  $C\left(x\right)=23.20-2\Vert -\left(x-1\right)\Vert$

Graph for Appropriate model is

  

Explanation of Solution

Give information:

Given:

Price of sending packages from New York to Atlanta is $\$23.20$ .

Calculation:

The cost of sending packages overnight is $\$23.20$ for a package of weighing up to but not including $1$ pound and additional $\$2$ are changed for additional pound or portion of pound.

That is the cost of package for the first up to $1$ pound is $\$23.20$ an cost increases $\$2$ when the next pound design. Then the cost is $\$23.20$ and there is step of $1$ pound for every $\$2$ to be added to it.

Then, the cost of $C$ of package as a function of weight $x$ can be given by model,

  $C\left(x\right)=23.20-2\Vert -\left(x-1\right)\Vert$

Calculate the values for verify the model,

$x$	$C\left(x\right)$
$1$	$23.2$
$1.25$	$25.2$
$1.5$	$25.2$
$2$	$25.2$
$2.5$	$27.2$
$3$	$27.2$
$3.5$	$29.2$
$4$	$29.2$

The values obtained verify that the model fits the given data,

Graph for the function is,