The  cost  of  a  machine  depreciates  every  year  and  can  be  modeled  using  the  function  c  (x  )  =  800(0.95)  x,  where  c  (x  )  is  the  cost  of  the  machine,  in  dollars,  x years  after  it  was  bought.  the  owner  of  the  machine  claims  that  the  cost  of  the  machine decreases  by  $40  every  year.  is  the  claim  correct?   explain.

Given that the model for machine depreciation is:
C(x)=800(0.95)^x
to evaluate the amount in cash that the machine depreciates at we let x=1, this will represent 1 year that we want to determine. Thus we shall have:
C(1)=800(0.95)^1
C(1)=$760
thus the amount of depreciation is:
800-760
=$40
Therefore we conclude that the machine depreciates at $40 per year. The claim is correct.