SOLUTION: A machine is now worth $155,800 and will be depreciated linearly over a 10 year period, at which time it will be worth $40,300 as scrap. (a) Find the rule of depreciation functio

Algebra ->  Finance -> SOLUTION: A machine is now worth $155,800 and will be depreciated linearly over a 10 year period, at which time it will be worth $40,300 as scrap. (a) Find the rule of depreciation functio      Log On


   

Question 1094142: A machine is now worth $155,800 and will be depreciated linearly over a 10 year period, at which time it will be worth $40,300 as scrap.
(a) Find the rule of depreciation function f.
​(b) What is the domain of​ f?
(c) What will the machine be worth in 7 years?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in years, starting now at +t=0+
Plot +t+ on the horizontal
Plot +f+ on the vertical
You are given 2 points on a line,
( 0, 155800 )
( 10, 40300 )
-------------------------------
(a)
Use the general point-slope formula
+%28+f+-+40300+%29+%2F+%28+t+-+10+%29+=+%28+155800+-+40300+%29+%2F+%28+0+-+10+%29+
+%28+f+-+40300+%29+%2F+%28+t+-+10+%29+=+115500+%2F+%28-10+%29+
+%28+f+-+40300+%29+%2F+%28+t+-+10+%29+=+-11550+
+f+-+40300+=+-11550t+%2B+115500+
+f+=+-11550t+%2B+155800+
------------------------------------
check:
does it go through ( 10, 40300 ) ?
+40300+=+-11550%2A10+%2B+155800+
+40300+=+-115500+%2B+155800+
+40300+=+40300+
OK
--------------
(b)
The domain is from ( 0, 155800 ) to ( t, 0 )
+0+=+-11550t+%2B+155800+
+11550t+=+155800+
+t+=+13.49+ yrs
The domain is from 0 to 13.49
-------------------------------
(c)
Find ( 7, f )
+f+=+-11550%2A7+%2B+155800+
+f+=+-80850+%2B+155800+
+f+=+74950+
It is worth $74,950 in 7 yrs
------------------------------
check the math