SOLUTION: a) In 2006 a new Ford Focus costs $15,574. The value of a focus decreases exponentially over time. Write a Formula for the value of a Focus that was new in 2006. (You don't know th

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: a) In 2006 a new Ford Focus costs $15,574. The value of a focus decreases exponentially over time. Write a Formula for the value of a Focus that was new in 2006. (You don't know th      Log On

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Question 1058294: a) In 2006 a new Ford Focus costs $15,574. The value of a focus decreases exponentially over time. Write a Formula for the value of a Focus that was new in 2006. (You don't know the value of the decay factor yet).
So would I use this formula: P%28t%29=P%5Bo%5Db%5Et
P(2006)= 15,574(1-b)^1
b) A 2 year old Focus costs $11,788. Find the decay factor and percent rate of depreciation.
c)How much would a 4 year old Focus cost?
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
b will contain the decay factor if you are using that formula shown. You have two points, (t,P). Try re-handling the variable so you have t=0 for year 2006 and t=2 for year 2008. Your two points are (0,15574) and (2,11788).

You choose the base you want, but log%28%28P%29%29=log%28%28P%5Bo%5D%29%29%2Blog%28%28b%5Et%29%29

log%28%28P%29%29=t%2Alog%28%28b%29%29%2Blog%28%28P%5Bo%5D%29%29, but not sure if this is necessary.

Look at the second point:
11788=15574%2Ab%5E2
b%5E2=11788%2F15574
b%5E2=0.7569026
highlight%28b=0.87%29 for model as highlight%28P%28t%29=15574%280.87%29%5Et%29.

You can break the b into its percents pieces as 1.00-0.13. This is a yearly decrease of 13%.

The four-year value would be the evaluation P%284%29=15574%2A%280.87%29%5E4.