SOLUTION: In 2010 your car was worth $12,000. In 2012 your car was worth $8,700. A)Suppose the value of your car decreased at a constant rate of change. Write a function f that determines

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: In 2010 your car was worth $12,000. In 2012 your car was worth $8,700. A)Suppose the value of your car decreased at a constant rate of change. Write a function f that determines       Log On


   

Question 1129312: In 2010 your car was worth $12,000. In 2012 your car was worth $8,700.
A)Suppose the value of your car decreased at a constant rate of change. Write a function f that determines the value of your car (in dollars) in terms of the number of years t since 2010.
B)Suppose the value of your car decreased exponentially. Write a function g that determines the value of your car (in dollars) in terms of the number of years t since 2010.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
A)
Let +t+ = yrs since 2010
slope = +m+
+m+=+%28+8700+-+12000+%29%2F2+
+m+=+-3300%2F2+
+m+=+-1650+
The vertical intercept must be +12000+, since
that is the value when +t=0+
+f%28t%29+=+-1650t+%2B+12000+
------------------------------------
B)
+g%282%29+=+8700+
+8700+=+12000%2A%28+1+-+r+%29%5E2+
+.725+=+%28+1+-+r+%29%5E2+
+1+-+r+=+sqrt%28+.725+%29+
+1+-+r+=+.85147+
+r+=+.1485+
----------------------
+g%28t%29+=+12000%2A%28+1+-+.1485+%29%5Et+
check:
+t+=+2+
+g%282%29+=+12000%2A.85147%5E2+
+g%282%29+=+12000%2A.725+
+g%282%29+=+8700+
OK