How Long Until a New SUV Depreciates Below 40% of Its Original Value?

[hallowon]

So we are currently doing sequences ie discrete functions for my functions class, and i came across this problem

The value of a new sports utility vehicle depreciates at a rate of 8%
per year. If the vehicle was bought for $45 000, when is it worth less than 40%
of its original value?

now i tried to use it sequential wise, but it failed me.
I then tried to solve it using exponential functions way, that too was a failure -_-

 

[dx]

What does "use it sequential wise" mean? Show your work so we can see where you went wrong and help you out.

 

[hallowon]

well here's what i did using exponential functions

T(n)=45 000(0.92)^n
40% of 45 000 is 18 000
so
18 000=45 000(0.92)^n
18000/45000=0.92^n

this is the point where i am stuck at. I cannot use logarithmic to solve this due to the fact that the curriculumn shifted it till next year.

Using my current knowledg of sequences this is what i got

tn=45000(0.92)^n-1
which is very similar too my exponential way ,but... looks wrong, and i don't know how to go from there:/

 

[dx]

well here's what i did using exponential functions

T(n)=45 000(0.92)^n
40% of 45 000 is 18 000
so
18 000=45 000(0.92)^n
18000/45000=0.92^n

this is the point where i am stuck at. I cannot use logarithmic to solve this due to the fact that the curriculumn shifted it till next year.

This is correct. Are you sure you're not allowed to use logarithms?

 

[hallowon]

yes, I live in ontario, Canada ,and teacher wants us not to use logarithmic because of curriculumn changes. However, we are in the discrete functions unit, and therefore it kinda insininuates us to find the answer using recursive,arithmetic, and.or geometric sequences using their general form.Anyway, The answer seems to be around 11 ish; however, how do u find that without doing logarithmic?

 

[Mark44]

If for some reason you're not allowed to use logarithms, you could use a calculator to calculate .92ⁿ for various values of n, stopping when you get close enough to 18/45 = 2/5 = .4

EDIT: Fix silly arithmetic error.