Question

Automobiles generally depreciate 14% per year. Hamid purchased a Smart Car for $25 000. (5 marks)
Create an equation that represents the value of this new vehicle over time, in years.
What would its value be after 20 years?
How long will it take for the Smart Car to lose three-quarters of its original value?

Answer 1

@tkhunny

Answer 2

Give it a go. Show at least the first year.

Answer 3

I have no idea where to start :( @tkhunny

Answer 4

I never believe that. It simply cannot be true. Have you EVER heard the word "Depreciate"? What does Depreciation do?

Answer 5

it goes down

Answer 6

@tkhunny

Answer 7

Perfect. If it depreciates 14%, HOW MUCH does it go down?

Answer 8

by 14%

Answer 9

0.14

Answer 10

@tkhunny

Answer 11

It's not necessary to tag me every time.

14% = 0.14 is the RATE that it goes down. What is the AMOUNT that it goes down?

Answer 12

the smart car and btw I tag you so you see this quicker

Answer 13

I see it just as quickly when you post ANYTHING. If you tag, that just means i see it twice.

You didn't answer my question. What AMOUNT does the value decrease in the first year?

Answer 14

25,000

Answer 15

No, $25,000 is the total value a the beginning of the 1st year. The value then decreases by 14%. What is 14% of $25,000?

Answer 16

its' 3500

Answer 17

One more time. What AMOUNT does the value decrease in the 1st year?

Answer 18

I dont get it

Answer 19

@tkhunny

Answer 20

I dont understand what you mean

Answer 21

$25,000
Depreciates 14% annually.
$3500 is 14% of $25,000

What is the value after $25,000 depreciates $3,500?

Answer 22

ohhh 21500

Answer 23

what is the equation

Answer 24

??

Answer 25

25000 - 3500 = 21500

NOw, use the EXACT same PATTERN to calculate the AMOUNT of depreciation in the 2nd year and the total value after the 2nd year.

Answer 26

I did it three times

Answer 27

@tkhunny

Answer 28

HOW DO I FORM AN EQUATION FROM HERE ??????

Answer 29

You must answer my question.

NOw, use the EXACT same PATTERN to calculate the AMOUNT of depreciation in the 2nd year and the total value after the 2nd year.

It doesn't do any good to tag me if you are not going to answer my questions. We need to get a feel for how it works. This is how we LEARN to formulate equations.

Answer 30

THE VALUE WOULD BE $18490 AFTER THE SECOND YEAR

Answer 31

@tkhunny

Answer 32

Okay, now one more thing before building the equation becomes natural. EXACTLY how did you obtain the correct answer $18,490 from $21,500?

Answer 33

I multiplied 21500 by 0.14

Answer 34

Now can we make the equation? @tkhunny

Answer 35

That's not correct. 21500*0.14 = 3010

I don't see 18490, yet.

Answer 36

oh then I subtracted 21500-3010

Answer 37

Okay, here we go.

We have:

Year 1

25000 * 0.14 = 3500
25000 - 3500 = 21500

Year 2

21500 * 0.14 = 3010
21500 - 3010 = 18490

Do you agree that this is the complete solution for the first two years?

Answer 38

yes

Answer 39

@tkhunny

Answer 40

Can you rewrite both of those years in such a way that we do NOT see the exact amount of the depreciation? Somehow, combine the two steps of the process into a single step that goes straight to the final amount?

Answer 41

idk how to

Answer 42

come on help me

Answer 43

I'll give you five minutes to think about it and produce a possible result.

Answer 44

25000x - 0.14

Answer 45

idk what Im doing

Answer 46

That's pretty good. Not quite, but you are in the neighborhood.

Year 1

25000 * 0.14 = 3500

25000 - 3500 = 21500

Look at that bottom equation.

25000 - 3500 = 21500

Can you think of another expression for 3500?

Answer 47

3500x -0.14 ??

Answer 48

its wrong I know

Answer 49

That makes no sense. Look at the first equation.

25000 * 0.14 = 3500

Can you see TWO ways to write 3500?

Answer 50

ya

Answer 51

Okay, now rewrite this equation using some other expression for 3500.

25000 - 3500 = 21500

Answer 52

so wait is that the equation you wanted me to write ?

Answer 53

Rewrite this equation using some other expression for 3500.

25000 - 3500 = 21500

Answer 54

2500- 1000=21500

Answer 55

What is that?

2500 - 1000 = 1500 - That's not 3500
21500 is not 3500.

Rewrite THIS equation using some other expression for 3500. Keep in mind that we know that 3500 = 25000 * 0.14

25000 - 3500 = 21500

Answer 56

I see. It's a typo.

Somehow, you meant 25000 - 1000 = 21500. This, of course, makes no sense, since 25000 - 1000 = 24000.

Any way...

25000 - 3500 = 21500

From the other equation, we have

25000 - (25000*0.14) = 21500

This needs to make sense.