Hey there! Hello!
Lets start with question one. You can see the costs of each car and the amount that they depreciate as soon as they're driven off the lot. All you need to do for these is convert the percentages to decimals, then multiply the number you get by the total cash amount for the car. This is how much the money will decrease, so you'll have to subtract it from the original amount. I'll show you what I mean:
[tex](30,000)(0.20)=6,000[/tex]
[tex]30,000-6,000=24,000[/tex]
You can use these steps to figure out the other.
For question two, all you need to do is subtract the amount that the chart says each car depreciates every year, then fill in the blank chart with the corresponding information. For example:
[tex]24,000-2,000=22,000[/tex] (first year)
[tex]22,000-2,000=20,000[/tex] (second year)
...and so on.
For the third question, you need to calculate the rate of change for both of the cars. You can do this by thinking of each year and its corresponding dollar amount as a point on a plot, like so:
(1, 22,000) and (2, 20,000)
Plug these into the slope formula, y2–y1 / x2–x1
[tex]20,000-22,000/2-1=(-2000)/1=(-2000)[/tex]
For question 4, you need to make an expression to show this function. Remember that you started off taking 0.20 off of the initial amount of the car, then subtract 2000 for every year. Let x represent the amount of years:
[tex](30,000)-(30,000)(0.20)-2000x=24,000-2000x[/tex]
From here, you can calculate the car's value all the way to 15 years for question 5, allowing you to complete the graph. This parts pretty simple, since it's been revealed for the first car that it goes down by $2000 every year and it's just a straight line.
For the interpretation part, I'm pretty sure your x–intercept is going to mean that the car is no longer worth money and your y–intercept is the amount the car started out as, which, in the case of the first car, is 24,000. I believe this is the same for the second car, as well.
I think that's about it? Keep in mind that everything above is for the first car. I know you can figure out everything for the second car based on what I've given you, but if something is stumping you, feel free to ask me any additional questions.
–Lamb :-)
