Question

NOOOOOOOOOTES (Review when needed)

Answer 1

Start by finding 16% of 50,000

Answer 2

what is 16% in decimal form?

Answer 3

no sorry, it is .16

Answer 4

are you allowed to use a calculator?

Answer 5

Ok, if you are allowed to use a calculator, then, to find 16% of something, you just multiply that something times .16.

Answer 6

nope. But its the first step.

Answer 7

8000 is how much the car depreciated in the first year. Your question is how much has it depreciated by the 4th year.

Answer 8

so 50,000 - 8000 is 42,000. The car at the end of year 1 is worth 42,000. Now, what about year two? Hint: they tell you it goes down by 16% each year.

Answer 9

And that is incorrect. Consider this. If I have 100 cookies, and you take 16%, I have 84 left. Now if you take 16% of my 84 cookies. Thats not 16 cookies anymore, because the starting amount is smaller. Does that make sense?

Back up to year 1. We took away 16% of 50000. which was 8000. Now at the start of year two, we only have 42000 to start with. 16% of 42000 will be smaller.

Answer 10

16% of 42000 is what?

Answer 11

What did we do with the 8000?

Answer 12

Perfect! So this year (year 2) we subtract from the current value.

Answer 13

Yep!

Answer 14

And I bet you can guess what we do for year 3.

Answer 15

yes, and so finally, after you subtract that, we have the value of the car at the end of 4 years.

Answer 16

Nice work. I feel like you got the hang of that. Does it feel like it makes sense? Why the 16% was getting smaller each year?

Answer 17

yes thank you very much :)

Answer 18

Welcome.

Answer 19

Ok. This might look a little different then the last one, but I promise you it is nearly the same. Do exactly what we did above, but this time, the keyword is GROWING. How do you think that word makes this different?

Answer 20

Exactly.

Answer 21

No. There's an easier way.

Answer 22

So, in the last question, we were taking 16% away from the total each year. Another way to think about that, is, we are leaving ourselve 84% of the total. 100%-16% = 84%

Answer 23

If you multiply 50,000 by .84, you get 42000, without having to subtract.

Answer 24

See how that saves us a step? ( I know what your thinking, but I did the .16 and subtract so you'd understand why it was working)

Answer 25

Now, if you multiply 42000 by .84 youll get the next value and so on. So the trick is. If you want to know how much the car depreciates after 4 years, you can multiply the starting amount by .84^4 .

Answer 26

just like x * x = x^2 , .84 * .84 = .84^2 see?

Answer 27

So you can just do \[50,000 * (.84)^{4}\]

Answer 28

very good intuition. The only problem is .93 is only 93% of the total. Since the population is growing, in year two, you will have 107% of what you did last year. So you'll want to change that .93 to 1.07

Answer 29

\[20,000*(1.07)^{x}\] where x is?

Answer 30

yup!