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 ?
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(3) = 131 ....so....
b. [187 - 131] / 2 = [56/ 2} = +$28M per year