SOLUTION: The population of a village can be modelled by the function P(x)= -22.5x^2+428x+1100, where x is the number of years since 1990. According to the model, when will the population be

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The population of a village can be modelled by the function P(x)= -22.5x^2+428x+1100, where x is the number of years since 1990. According to the model, when will the population be      Log On


   

Question 1032942: The population of a village can be modelled by the function P(x)= -22.5x^2+428x+1100, where x is the number of years since 1990. According to the model, when will the population be the highest?
Much appreciated
Found 2 solutions by Cromlix, stanbon:
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,
P(x) = -22.5x^2 + 428x + 1100
To find maximum, differentiate:
P'(x) = -45x + 428
P'(x) = 0
-45x + 428 = 0
-45x = -428
x = -428/-45
x = 9.51
Nature Table:
......................... - 9.51 +
-45x + 428....... + 0 -
............................ / - \
Maximum.
Therefore after 9.5 years the population
will be at its maximum.
-22.5(9.5) + 428(9.5) + 1100
= 4952.
Hope this helps :-)

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The population of a village can be modelled by the function P(x)= -22.5x^2+428x+1100, where x is the number of years since 1990. According to the model, when will the population be the highest?
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Max occurs when x = -b/(2a) = -428/(2*-22.5) = -428/45 = 9.511...
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Ans: 1990 + 9.5111 is in the year 2000
Cheers,
Stan H.