Math Is Fun Forum

reallylongnickname

Member

Registered: 2011-03-30

Posts: 50

Exp func application

A new car costs $24000. It loses 8% value every 6 mths. The formula is;

What would be the half life formula of the car in years? The value would be $12000.

Last edited by reallylongnickname (2011-04-17 15:21:21)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Exp func application

Hi reallylongnickname;

I might be missing something here but it looks like you are solving for t.

t = 49.877702...

So I do not understand what you want with the second formula?!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

reallylongnickname

Member

Registered: 2011-03-30

Posts: 50

Re: Exp func application

It's solved it for months, but what if I wanted it solved in years?

Last edited by reallylongnickname (2011-04-17 20:59:36)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Exp func application

Hi;

I think it is solved not in months but in groups of 6 months. So I would divide t = 49.877702 by 2 to get years.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

reallylongnickname

Member

Registered: 2011-03-30

Posts: 50

Re: Exp func application

If divided 49.877702 by 12, the answer is 4.16 years. To actually use the method I used above, I would probably change the

to 2t or something.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Exp func application

Doing the calculation as a difference eqaution. I get:

24000.,22080.,20313.6,18688.512,17193.43104,15817.9565568,14552.520032256,13388.31842967552,12317.25295530148,11331.87271887736

It goes below 12000 on a little bit more than the 8th 6 month period. Which means a little more than 4 years. So your answer agrees.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,163

Re: Exp func application

hi reallylongnickname

I'm puzzled by your first equation

What exactly is 't' here?

A new car costs $24000. It loses 8% value every 6 mths.

So I'll have h = number of half years

You want to know how many half years will it be before the value drops to 12000

This can be turned into years y = h/2 = 4.156475

If you want a formula in years rather than half years

x 0.92 very half year means x 0.92^2 = 0.8464 for every year

so the formula becomes

where y is the time in years.

then

and so

Bob

Last edited by Bob (2011-04-17 23:16:26)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

reallylongnickname

Member

Registered: 2011-03-30

Posts: 50

Re: Exp func application

Log is more efficient, but anyway, the t/6 is # of periods (time in months).