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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

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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