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a hospital's revenue (in millions of dollars) is projected to be R(x)=7x^2-3x+18 and its costs (in millions of dollars) are projected to be C(x)=3x^2+x-89 where x represents the number of years into the future. a. create the profit function for the hospital. b. what is the average rate of change in the profit from year 3 to year 5 ?

Guest Apr 9, 2017
 #1
avatar+90088 
+2

Profit = Revenue - Cost   ...  so...

 

P(x)  = R(x) - C(x)

 

[ 7x^2-3x+18 ] - [ 3x^2+x-89 ]  =

 

a.  P(x)  =  4x^2 - 4x + 107

 

Avg Rate of Change from Year 3 to 5   =

 

[ P(5)  - P(3) ]  / [ 5 - 3]

 

P(5)  =187

P(3)  = 131   ....so....

 

b.  [187 - 131] / 2    = [56/ 2} =   +$28M  per year

 

 

cool cool cool

CPhill  Apr 10, 2017
 #2
avatar+7324 
+2

Hmmm....that's funny how if you try the cost function with years between 0 and 5 you get a negative cost...??

 

That's a pretty good deal they got then!!  laughlaugh

hectictar  Apr 10, 2017

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