SOLUTION: Hello! I've been having some trouble with the following word problem A large pond is stocked with fish. The fish population P is modeled by the formula P = 4t + 8√t + 1

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Question 196819: Hello!
I've been having some trouble with the following word problem
A large pond is stocked with fish. The fish population P is modeled by the formula P = 4t + 8√t + 110, where t is the number of days since the fish were first introduced into the pond. How many days will it take for the fish population to reach 500?
thanks!
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Is the given equation ???

Start with the given equation.


Plug in


Subtract 4t from both sides.


Square both sides


Square the square root to eliminate it.


FOIL


Get all terms to the left side.


Combine like terms.


Notice we have a quadratic in the form of where , , and


Let's use the quadratic formula to solve for t


Start with the quadratic formula


Plug in , , and


Negate to get .


Square to get .


Multiply to get


Subtract from to get


Multiply and to get .


Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


or Break up the expression.


or Use a calculator to approximate


Now because plugging in back in the second equation results in a contradiction, this means that is NOT a solution.


So the only solution is approximately


This means that it will take about 122 days (rounding up to the nearest whole number) for the fish population to reach 500.
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