You buy a new car for $32,000. The value of the car decreases by 12% each year.
a. Write a rule for the average yearly value of the car (in dollars) in terms of the current year.
Let n=the current year.
b. In about how many years will the value of the car fall to $13,077?

I think this was a geometric sequence and so I used :
an = a1(r)^(n-1)
an = 32000(-.12)^(n-1) and this is my rule.

Then I put 13077 in an and solved
13077 = 32000(-.12)^(n-1)

13077/32000 = -.12^(n-1)
log 13077/32000 = log-.12^(n-1)

log13077/32000/log-.12 = n – 1

log13077/32000/log-.12 +

Question

You buy a new car for $32,000.  The value of the car decreases by 12% each year.
	a.  Write a rule for the average yearly value of the car  (in dollars) in terms of the current year. 
	      Let n=the current year.
	b.  In about how many years will the value of the car fall to $13,077?

I think this was a geometric sequence and so I used :
an = a1(r)^(n-1) 
an = 32000(-.12)^(n-1) and this is my rule.

Then I put 13077 in an and solved
13077 = 32000(-.12)^(n-1)

13077/32000 = -.12^(n-1) 
log 13077/32000 = log-.12^(n-1) 

log13077/32000/log-.12 = n – 1

log13077/32000/log-.12 +

anonymous · Answer

@dpaInc pl help..the quest been up for 5 hrs nw..

anonymous · Answer

sorry man... i really can't think anymore... it's 1 am here... i'm gonna get some shut eye...

anonymous · Answer

its ok..thankx for comming tho.

anonymous · Answer

i'll check up on this tomorrow...

anonymous · Answer

tankx again ;)

@kropot72  any hpe?

kropot72 · Answer

Sorry, 
 I need time to think on this one.

anonymous · Answer

itz okay tak ur tym

tommo_lcfc · Answer

I can help you!

Now the first thing to note is that if the price decreases by 12% each year, this is equivalent to 88% each year (100-12 = 88). As it decreases, the ratio is 0.88. If it was increasing by 12%, the ratio would be 1.12. Common ratios can never be negative.

So the nth term is 32000 x 0.88^(n-1).

Equate this to 13077.

So 13077 = 32000 x 0.88^(n-1)

13077/32000 = 0.88^(n-1)

log(13077/32000) = (n-1) log (0.88)

n-1 = log(13077/32000) / log(0.88) = 7.000370328.

So n = 8.000370328 = 8 years.

Do you get that?