Question

10) The resale value of a machine decreases
over a 10 year period at a rate that depends
on the age of the machine. When the
machine is x years old, the rate at which
its value is changing is 2200 (x - 10) per
year. Express the value of the machine as a
function of its age and initial value. If the
machine was originally worth * 1,20,000
how much will it be worth when it is 10
years old?​

Answer 1

Answer:

Let y be the value of machine when machine is x years old

according to the given condition ,

dy/dx 2200 (x-10)

dy=2200 (x-10 ) dx

Integration on both sides we get

1 dy =2200 (x-10) dx

`y =2200 (x^2/2 -10x)+c

y=1100 x2 -22000x+c

when x=o,y=120000

12000=1100(0)²-

22oo(0)+c

c=120000

the value of the machine can be expressed

as a function of its age as

y=1,100x²-22000x+120000

initial value x-o,y=

120000

when x=10

y=1,100 (10)²-22000(10)+120000

=10000

the machine will worth $10000

when it is 10 years old