Chapter 2.4, Problem 26E

a.

To determine

Determine what type of function you can use to model the data.

Answer to Problem 26E

Function is a linear equation or a line $y=4x.$

Explanation of Solution

Given information: The table shows the distances y a motorcyclist is from home after x hours.

  

Calculation Because first differences are constant so we can modal the data with a linear function

$f(0)$		$f(1)$		$f(2)$		$f(3)$
0		45		90		135
	-45		-45		-45

  $f(x)=ax+b.$

  $\begin{array}{l}f(0)=a\times 0+b.\\ 0=0+b\\ b=0.\\ f(1)=a\times 1+b.\\ 45=a+0.\\ a=45.\\ f(x)=45x+0.\\ f(x)=45x.\\ y=45x.\end{array}$

b.

To determine

Write and evaluate a function to determine the distance the motorcyclist is from home after 6 hours.

Answer to Problem 26E

  $\begin{array}{l}f(x)=45x.\\ f(6)=270.\end{array}$

Explanation of Solution

Given information: The table shows the distances y a motorcyclist is from home after x hours.

  

Calculation Because first differences are constant so we can modal the data with a linear function

$f(0)$		$f(1)$		$f(2)$		$f(3)$
0		45		90		135
	-45		-45		-45

  $f(x)=ax+b.$

  $\begin{array}{l}f(0)=a\times 0+b.\\ 0=0+b\\ b=0.\\ f(1)=a\times 1+b.\\ 45=a+0.\\ a=45.\\ f(x)=45x+0.\\ f(x)=45x.\\ y=45x.\end{array}$

So,$f(6)=45\times 6=270$.