SOLUTION: Can someone please check if I did this right? A machine is now worth $159,500 an will be depreciated linearly over a 9 years period, at which time it will be worth $43,760 as sc

Question 1096558: Can someone please check if I did this right?
A machine is now worth $159,500 an will be depreciated linearly over a 9 years period, at which time it will be worth $43,760 as scrap.
a) Find the rule of depreciation function f?
b) What is the domain of f?
c) What will the machine be worth in 5 years?
___________________________________________________
a) f(x)=-115,740x+159,500
b) Domain should be from 0, 159500 to ??? (I don't know)
c)I used this formula: y=mx+b
First, I found m= 43,760-159,500/9-0=-115,740/9==12,860
Then y= - 12, 860(5)+159,500=-95,200
Is it -95,200 correct result? I'm not sure. Thank you for your help and explanation.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let's look at your answer for part c first.

You correctly found the slope by dividing the change in value by the number of years; the slope is -12,860. That means the value is decreasing by $12,860 each year. Then you found out how much the value would decrease over a 5 year period, and you subtracted that amount from the original value. Exactly right.

So you are good on part c.

Now go back to part a. The function you show suggests that the entire depreciation occurs in 1 year. What you want in your function is the slope you calculated in part c. So

Note that this is the standard "y=mx+b" form of the equation. It is called standard form because it is the form that makes it easiest to use the equation in calculations. But for a final answer to a question like this, a better form might be

because then it is easier to see that the meaning of the function is that the initial value if $159,500 and then the value decreases by $12,860 each year.

And finally part b.

Note that the domain is the set of x values, not the set of y (function) values. Since the problem says the machine is considered scrap after 9 years, the domain is from 0 to 9.

The answer you tried to give for this part is the range (set of y values). And again, since the machine is considered scrap after 9 years, the range would be from $43,760 to $159,500, not 0 to $159,500.

And technically, in mathematics when we state the range, we always go from lowest y value to highest, as in the previous paragraph. But in this problem, speaking informally, it would make sense to say the range is from 159,500 to 43,760.
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