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Answer:
g(t) = 10000(0.938)^t
Step-by-step explanation:
Given data:
car worth is $10,000 in 2012
car worth is $8000 in 2014
let linear function is given as
P(t) = at + b
which denote the value of car in year t
take t =0 for year 2012
at t =0, 10,000 = 0 + b
we get b = 10,000
take t =2 for year 2014
at t =2, P(2) = 2a + b
8800 = 2a + 10,000
a = - 600
Thus the price of car at year t after 2012 is given as p(t) = -600t + 10000
let the exponential function where t denote t = 0 at 2012
putting t = 0 P(0) = 10,000 we get 10,000 = ab^0
a = 10,000
putting t = 2 p = 8800
b = 0.938
g(t) = 10000(0.938)^t