OpenStudy (anonymous):

NOOOOOOOOOTES (Review when needed)

3 years ago
OpenStudy (anonymous):

Start by finding 16% of 50,000

3 years ago
OpenStudy (anonymous):

what is 16% in decimal form?

3 years ago
OpenStudy (anonymous):

no sorry, it is .16

3 years ago
OpenStudy (anonymous):

are you allowed to use a calculator?

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

nope. But its the first step.

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

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.

3 years ago
OpenStudy (anonymous):

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.

3 years ago
OpenStudy (anonymous):

16% of 42000 is what?

3 years ago
OpenStudy (anonymous):

What did we do with the 8000?

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

Yep!

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

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?

3 years ago
OpenStudy (anonymous):

yes thank you very much :)

3 years ago
OpenStudy (anonymous):

Welcome.

3 years ago
OpenStudy (anonymous):

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?

3 years ago
OpenStudy (anonymous):

Exactly.

3 years ago
OpenStudy (anonymous):

No. There's an easier way.

3 years ago
OpenStudy (anonymous):

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%

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

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)

3 years ago
OpenStudy (anonymous):

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 .

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

yup!

3 years ago