Colleen's station wagon is depreciating at a rate of 9% per year. She paid $24,500 for it in 2002. What will the car be worth in 2008 to the nearest hundred dollars?

1 Answer
Shura
Jun 4, 2015

We have a geometric sequence :

u_1 = 24500
u_(n+1) = u_n - u_n * 9/100 = u_n * 91/100

=> u_n = u_1 * r^(n-1), where r = 91/100 and u_n gives you the worth of the car in the year n.

=> u_n = 24500 * (91/100)^(n-1)

n = 1 = year 2002 => n = 7 = year 2008

=> u_7 = 24500 * (9/100)^6 ~~ 13900 $ in 2008.

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