Question 1079429: A computer that, when purchased 5 years ago cost $5,000 now has a value of $1,100. Find the value of the computer after 8 years by using the exponential model V(t) = V_0e^kt, in which V(t) is the value of the computer at any time t, V_0 is the initial cost, and t is the time in years. Round your answer to the nearest hundredth. Any help is appreciated (:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Formula
V(t) = V_0e^kt,
1100 = 5000 *e^5k
1100/5000 = e^5k
take the natural log of both sides
ln(1100/5000) = ln(e^(5k))
ln(1100/5000) =5k
k = ln(1100/5000) / 5 = -.3028255465 (decay constant)
Vt= V0 * e^(kt)
t=8 , V0 =5000, k we have found out
Plug the value of in Vt = pV0* e^(kt) = 5000*e^(0-.3028255465*8)=443.45
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