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Problem 9 Hard Difficulty

The graph of a straight line depreciation equation is shown.
a. Use the graph to approximate the value of the car after 4 years.
b. Use the graph to approximate the value of the car after 5 years.
c. Use the graph to approximate when the car will be worth half its original value.


a. $y=-3,200 x+25,600$
$\$ 12,800$
b. $\$ 9,600$
c. 4 years


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Video Transcript

first thing you should notice if you look at my graph is that I have a lot more numbers here and I need to talk about how I got that. It's counted by 3200 and you see that 16,000 there. Well, there's five sections. 1234 It's like the fifth in line to get to 16,000 meaning If I divide this by five, that's where. Actually, I got that 3200 that were counting by and it turns out toe work. And it doesn't break the pattern if I continue going up. And so we immediately see that the value of this vehicle is $25,600 so we can write our equation. Do using this, except there's actually one more thing we need to know. That's not super obvious is if we take 25,600 in divided by eight, right, because that's how long it's going to take. And actually let me write this, um, looking like a slope. Uh, this should be negative because that's how far the car is gonna decreasing value. This gives us negative 3200 so it's just kind of a coincidence that it also happens to be 3200. And the reason is it's 123456 708 spaces. If I include the 1st 1 and eight spaces in this direction as well, so the slope is negative. 3200. It was a coefficient of X, which is the years going by. And then we add the price of the car. 25,600. And there's our equation. I believe the next thing this is four years and so I'm gonna use this equation to say what would happen after four years? Well, I would just plug in a four here and 25 600 and so 3200 times for is what I'm gonna plug into my calculator. Riel, quick for you guys is negative. 12,800 some kind of run out of room. Maybe I should have done this in a different location, but plus 25,600 ends up being 12,800 which, interestingly enough, is the answer part. See, you can see it's decreased 12,800. It's now at the value of 12,800 it is half of the now you. Another way to say that 25,600 divided by two equals that 12,800. So I just answered. See, I went out of order. There's answer to a It's here and the answer to see is here. Which is I guess I should say, four years, because that's what they want to know. How long before it's half the value? Okay, five years. So now we're gonna take this equation and plug in five. And in fact, I'm going to send the tricky if I know that is decreasing 3200 every single year, and after four years, it's 12,800. Why not just subtract 3200? Cause then you'll find the price after the next year, the fifth year. So that's actually gonna save us some time. 9600 Is that difference? So here's our answer to part B M kind of putting dollar signs around everything, but, um, after five years, it will be 9600 because I can take the four years and subtract the Slope 3200 to get the next year's value. So there it is