Question

A motor scooter purchased for $1,000 depreciates at an annual rate of 15%. Write an exponential function, and graph the function. Use the graph to predict when the value will fall below $100.
(images attached)

Answer 1

@Tommynaut

Answer 2

So have you tried forming some sort of equation?

Answer 3

And those all looks like the same image...

Answer 4

I tried but I kept getting absurd answers. and the graphs are.... oh the other parts didn't copy, one second

Answer 5

I don't think you really need to post any more images.
Let's just start with our initial value: we have 1000. So our value/amount = 1000, or A = 1000. However, after each year, our value goes down by 15% of what it was before. The compound interest equation is something like
A = P(1+r)^n where A is the amount of money, P is the starting amount (let that be 1000 here), r is the rate, and n is the time period (years... we don't know how many though).

So, our equation would be A = 1000(1+r)^n and all we need to finish it off is knowing what r is. Can you give me a guess?

Answer 6

1) v(t)=0.85(1000),the value will fall below $100 in about 14.2 years.
2 )v(t)=0.85(1000), the value will fall below $100 in about 18 years.
3)v(t) =1000(0.85),the value will fall below $100 in about 18 years.
4)v(t)= 1000(0.85), the value will fall below $100 in about14.2 years

Answer 7

those were above the graphs

Answer 8

Oh right. Well, technically 1 and 4 are the same answer, as are 2 and 3, they're just written in different ways.

Answer 9

weird. oh and they also have ^t after the parentheses

Answer 10

Yeah, which makes sense... and means that 2 and 3 are not the same answer, and 1 and 4 are also not the same answer haha... that changes things.
So can you give me a guess what you thing the rate answer is? Explain your thinking.

Answer 11

honestly I have no clue

Answer 12

Well, I was saying before that the equation would generally be A = P(1+r)^n, where A is amount, P is principle (or initial) amount, r is the rate and n is the number of years.

If we adapt that to our current scenario, it would be v(t) = P(1+r)^t

P is 1000, right? It's what we start with.
If the rate is a depreciation of 15%, well we know that 15% = 0.15, but it's a depreciation, so it's -0.15, so 1-0.15 = what? 0.85, right?

So we have v(t) = 1000(0.85)^t

Now, looking at the graph, at that time (t) can you see the graph drop below 100?
That would give you the t value for v(t) = 100.
Trying plugging that t value back into your v(t) equation (use a calculator) to see if the answer is 100 (it probably won't be 100 but very close to it)

Answer 13

woah

Answer 14

Was some part of that a bit too confusing?

Answer 15

sort of was that the answer?

Answer 16

Well, from what I showed you, it's either 3 or 4, but it's up to you to work it out from the graph

Answer 17

you figure things out so fast I have been stuck on these all dang day

Answer 18

It might help if you went over your class notes to find the formulas :) what did you get as your final answer to this question?

Answer 19

im not sure the graphs look the same to mee xD

Answer 20

Yes, they are the same, that's the point. In one of the graphs (it doesn't matter which), for which value of (yr) is is $ = 100?

Answer 21

so it doesn't matter which one I chose?

Answer 22

Yep, it's the same graph

Answer 23

teachers always trying to confuse me

Answer 24

So, what did you get?

Answer 25

I chose 3

Answer 26

Why? Did you try putting t = 18 into the equation?

Answer 27

no? was I supposed too xD

Answer 28

It would have helped (and I did suggest it before...)

If you look on the graph, at about x = 14 your value is = 100, which is what you want. That's why the answer is 4, but you can check by putting 14.2 into the equation and seeing if you end up with a value close to 100.

Answer 29

ohhh I gottcha. that makes sense

Answer 30

Awesome

Answer 31

Thank you for all your help

Answer 32

No worries :)

Answer 33

do you think you will be on later?