Question

Jamaya is ready to trade in her car and purchase a newer model. The salesman at Burgess’ CarMart tells her that her car loses 20% of its value each year and that currently her car is worth only $2500. Jamaya paid $28,000 for her new car ten years ago and thinks that the salesman is trying to cheat her. She does the math and calculates that her car is worth at least $5000. Who, if anyone, calculated the value of the car correctly? Write a short paragraph explaining who is correct and show the geometric sequence which justifies your answer. @Psymon

Answer 1

I wish these were like the series I had to do, lol. These actually require more thought than I'm used to. Either way, did you try and come up with something or just lost? I can show ya what I was doing, but just curious :P

Answer 2

take 20% of the previous year's value. If the original value is 28,00, then the second year would be 28000-28000(.20)=22400; the second year would be 22400-22400(.20)=17920, and so on??

Answer 3

Right, you got the right idea. But if you put that into a regular geo-series form it'd come out kinda funky. As opposed to finding 20% then subtracting it, we need to put it in a series, which means something like ar^n. You've seen ar^n before, right?

Answer 4

Yeah, but I don't know how to do it.

Answer 5

Ah, gotcha. Well, a is basically your starting point. So in this case, 28,000. And each time, that 28,000 gets multiplied by some number r. The amount of times 28,000 is multiplied by r is what you put for n. In this case, n is also obvious, 10. Now its just figuring out what your r is. So far we would have 28000(r)^10. Following me so far?

Answer 6

Yeah.

Answer 7

Okay, awesome ^_^ Well, if we picked .20 as our r, we'd get an insanely small number. You put that in the calculator and you'll see it's off. So think of it this way. Instead of each time taking away 20%, how bout seeing how much you have left each time :P

Answer 8

...Go on

Answer 9

Well, if you lose 20%, then every year you're left with 80% of whatyou had the previous year. So if you want 80% of the previous year each time, you want r to be 80%. So your series would be 28000(4/5)^10

Answer 10

Ohhhhh :o

Answer 11

Mhm. You want 4/5 of each previous year. Not only isit moredirect to just find 80% instead of subtracting 20%, you can actually put it into the ar^n formula that way :P

Answer 12

Okay :o

Answer 13

xDD Mhm. Since you're dealing with geo-series, you can usually find some way to put it into an ar^n form or the form that prime showed ya earlier. I'm used to only doing these to infinity, so I dont remember the other formulas off the top of my head, lol.

Answer 14

So we just have to do 28000(4/5)^10 and then decide who is wrong and who is right?

Answer 15

Yep. In which theyre both wrong, lol. But thats exactly what youd do. And it makes sense, too.

Answer 16

Is it (28000 *4/5)^10
or 28000 * (4/5^10)

Answer 17

28000(4/5)^10. So (4/5)^10 first, then multiplied by 28000.

Answer 18

*wonders who came up with the name Jamaya*

Answer 19

I go to a black school..

Answer 20

Ah. Makes sense. Still though, it seems like math problems like to invent names O.o

Answer 21

Didnt mean to offend if I did, though >.<

Answer 22

No, I'm white XD

Answer 23

I don't really pay attention to the names. They're either really generic, or really weird.

Answer 24

Lol, okies. Yeah, not out to get on anyone's bad side, thats for sure o.o And you're the only one on here I talk to as opposed to just answer questions for, so rather not ruin that xD