Chapter 1, Problem 62RE

(a)

To determine

To find: The expression that gives the value $y$ after $x$ years.

Answer to Problem 62RE

The expression that gives the value $y$ after $x$ years is $100,000-10,000x$ for $0\le x\le 10.$

Explanation of Solution

Given information:

The given purchased an $18-$ wheel truck for $\$1000,000$ .

The truck depreciates at the constant rate of $\$10,000$ per year for $10$ years.

Calculation:

Calculate, the value of truck depreciates by a constant rate so the equation must be linear.

The truck start at $\$1000,000$ .

Thus, $y$ -intercept is $1000,000$ .

It is loses $\$10,000$ per year, so the slope is $m=-10,000$ .

Thus,

  $\begin{array}{c}y=mx+b\\ =-10,000x+100,000\\ =100,000-10,000x\end{array}$

For, $0\le x\le 10.$

Therefore, the expression that gives the value $y$ after $x$ years is $100,000-10,000x$ for $0\le x\le 10.$

(b)

To determine

To find: When the value of the truck is $\$55,000$ .

Answer to Problem 62RE

The value of the truck is $\$55,000$ in $4.5$ years.

Explanation of Solution

Given information:

The given purchased an $18-$ wheel truck for $\$1000,000$ .

The truck depreciates at the constant rate of $\$10,000$ per year for $10$ years.

Calculation:

Calculate the value of the truck,

$y=100,000-10,000x$	Take the expression for $y$ , the value of truck, from the previous part of the problem.
$55,000=100,000-10,000x$	We are told the value so plug in $55,000$ for $y$ .
$55=100-10x$	Divide both side by $1000$ .
$10x=100-55$	Rearrange to isolate $x$.
$x=4.5$ years	Solve for $x$ by dividing both side by $10$ .

Therefore, the value of the truck is $\$55,000$ in $4.5$ years.