Question

I’m having trouble with this problem please help?The second part of the question is at the beginning of the Answer Tab.

Answer 1

Finding the line equation

To answer this question, we have the following points for the line:

(2018, $3200) and (2020, $2000).

Since we want to find the relationship between the number of years after 2018, x, and the value of the computer, y, we need to have the year 2018 as the starting year, and we can replace it with 0. The rest of the years will be the number of years after 2018. For example, the year 2020 will be 2 years after 2018. The year 2022 will be 4 years after 2018 and so on.

Therefore, we have to find the equation of the line for the following points:

• (0, $3200), (2, $2000)

Then to find the equation line, we have to apply the two-point form of the line equation:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)_{}$

If we label each point first, we have:

$\begin{gathered} x_1=0,y_1=3200 \\ x_2=2,y_2=2000 \end{gathered}$

Now, we can substitute these values into the two-point form of the line equation:

$\begin{gathered} y-3200=\frac{2000-3200}{2-0}(x-0) \\ y-3200=\frac{-1200}{2}x \\ y-3200=-600x \\ y-3200+3200=-600x+3200 \\ y=-600x+3200 \\ f(x)=y=-600x+3200 \end{gathered}$

Therefore, the relationship between years after 2018 (x) and the value of the computer (y) is as follows:

$y=-600x+3200$

Estimating the value of the computer in the year 2022

We can see that the year 2022 is four (4) years after the year 2018:

$2022-2018=4$

Therefore, we can estimate the value of the computer in the year 2022 substituting x = 4 into the linear function:

$\begin{gathered} y=-600(4)+3200 \\ y=-2400+3200 \\ y=800 \end{gathered}$

Hence, the value of the computer, following this linear model is in the year 2022 of $800.

Estimating the value of the computer in the year 2024

We need to find the number of years in 2024 after 2018:

$2024-2018=6$

Now, we have to substitute this value into the linear equation as follows:

$\begin{gathered} y=-600x+3200 \\ y=-600(6)+3200 \\ y=-3600+3200 \\ y=-400 \end{gathered}$

We have that the value of the computer is -$400.

In this case, it does not have any sense to calculate this value. The item, in this case, is "creating" losses to the company (we can see it is a negative value), and we can sell the item before its value is zero. In a few words, it does not have any sense to calculate or estimate the value of the computer in 2024 because the item has become totally depreciated before that year.