Chapter 7.9, Problem 2P

To determine

To calculate: The value of automobile y years after it is purchased.

  $\begin{array}{ccccccc}\text{Years}& 0& 1& 2& 3& 5& 10\\ \text{Value}\left(V\right)& & & & & & \end{array}$

Answer to Problem 2P

The value of automobile y years after it is purchased is tabulated below.

  $\begin{array}{ccccccc}\text{Years}& 0& 1& 2& 3& 5& 10\\ \text{Value}\left(V\right)& 12000& 8571.429& 6122.449& 4373.178& 2231.213& 414.859\end{array}$

Explanation of Solution

Given information:

The relation $V=12,000{\left(1.4\right)}^{-y}$ depicts the value V of a new automobile $\$12,000$ , y years after it is purchased.

Calculation:

Consider the relation $V=12,000{\left(1.4\right)}^{-y}$ depicts the value V of a new automobile $\$12,000$ , y years after it is purchased.

To evaluate the value of automobile at present and after 1, 2, 3, 5 and 10 years, substitute as provided below.

Now, the value of automobile at present that is now is when $y=0$ substitute y as 0 in the above expression that is $V=12,000{\left(1.4\right)}^0$ .

With the help of calculator evaluate the value of expression.

  $\begin{array}{c}V=12,000{\left(1.4\right)}^0\\ =12,000\end{array}$

Now, the value of automobile after 1 year is when $y=1$ substitute y as 1 in the provided expression that is $V=12,000{\left(1.4\right)}^{-1}$ .

With the help of calculator evaluate the value of expression.

  $\begin{array}{c}V=12,000{\left(1.4\right)}^{-1}\\ =8571.429\end{array}$

Now, the value of automobile after 2 years is when $y=2$ substitute y as 2 in the provided expression that is $V=12,000{\left(1.4\right)}^{-2}$ .

With the help of calculator evaluate the value of expression.

  $\begin{array}{c}V=12,000{\left(1.4\right)}^{-2}\\ =6122.449\end{array}$

Now, the value of automobile after 3 years is when $y=3$ substitute y as 3 in the provided expression that is $V=12,000{\left(1.4\right)}^{-3}$ .

With the help of calculator evaluate the value of expression.

  $\begin{array}{c}V=12,000{\left(1.4\right)}^{-3}\\ =4373.178\end{array}$

Now, the value of automobile after 5 years is when $y=5$ substitute y as 5 in the provided expression that is $V=12,000{\left(1.4\right)}^{-5}$ .

With the help of calculator evaluate the value of expression.

  $\begin{array}{c}V=12,000{\left(1.4\right)}^{-5}\\ =2231.213\end{array}$

Now, the value of automobile after 10 years is when $y=10$ substitute y as 10 in the provided expression that is $V=12,000{\left(1.4\right)}^{-10}$ .

With the help of calculator evaluate the value of expression.

  $\begin{array}{c}V=12,000{\left(1.4\right)}^{-10}\\ =414.859\end{array}$

Thus, the value of automobile y years after it is purchased is tabulated below.

  $\begin{array}{ccccccc}\text{Years}& 0& 1& 2& 3& 5& 10\\ \text{Value}\left(V\right)& 12000& 8571.429& 6122.449& 4373.178& 2231.213& 414.859\end{array}$