SOLUTION: The profits of Mr. Unlucky’s company can be represented by the equation p(x)=-3x^2+18x-4 where p(x) is the amount of profit in hundreds of thousands of dollars and x is the numbe

Question 1152648: The profits of Mr. Unlucky’s company can be represented by the equation p(x)=-3x^2+18x-4 where p(x) is the amount of profit in hundreds of thousands of dollars and x is the number of years of operation. He realizes his company is on the downturn and wishes to sell before he ends up in debt.
a. When will Mr. Unlucky’s business show the maximum profit? ___ years
b. What is the maximum profit? ____ hundreds of thousands
c. During what time period will Mr. Unlucky expect his business’ profits to be on the downturn? After ___ years
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
maximum years would be where x=-b/2a or -18/-6 or x=3
put that into the equation to get p(3)=-27+54-4=23 hundreds of thousands.
from year 3 on, the profit decreases
the zero point is where f(x)=0
this is -3x^2+18x-4=0
or 3x^2-18x+4=0
quadratic formula
x=(1/6)(18+/-sqrt(324-48)); sqrt 276=16.61
x=(34.61/6)=5.77 years, so 2.77 years of decreasing profits.

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