SOLUTION: A new car costs 29,000 depreciates to 80% of its value in 4 years A.assume that the depreciation is linear what is the linear function that models the value if this car t years a

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: A new car costs 29,000 depreciates to 80% of its value in 4 years A.assume that the depreciation is linear what is the linear function that models the value if this car t years a      Log On

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Question 1142983: A new car costs 29,000 depreciates to 80% of its value in 4 years
A.assume that the depreciation is linear what is the linear function that models the value if this car t years after purchase?
B. Assume that the value of the car is given by an exponential function Ae^kt where a is the initial price of the car find the value of the constant k

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +V+ = the car's value after +t+ years
+V+=+-29000%2A%28+.2%2A%28t%2F4%29%29+%2B+29000+%29+
+V+=+29000%2A%28+1+-+.05t+%29+
------------------------------------
+V+=+A%2Ae%5E%28+k%2At+%29+
+V+=+29000%2Ae%5E%28+k%2A%28t%2F4%29%29+
When +t+=+4+, +V+=+.8%2A29000+
+23200+=+29000%2Ae%5Ek+
+e%5Ek+=+.8+
Take the natural log of both sides
+k+=+-.2231+
----------------------
check:
+e%5Ek+=+.8+
+e%5E%28-.2231+%29+=+.8+
+.8+=+.8+
OK
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