SOLUTION: I keep getting the incorrect answer to the following problem, I'm not sure where my error was, can you help me? A large pond is stocked with fish. The fish population P is model

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: I keep getting the incorrect answer to the following problem, I'm not sure where my error was, can you help me? A large pond is stocked with fish. The fish population P is model      Log On


   

Question 196644: I keep getting the incorrect answer to the following problem, I'm not sure where my error was, can you help me?
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 edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
4t+8sqrt(t)+110=500
4t-390=-8sqrt(t)
2t-195=-4sqrt(t)
4t^2-780t+38025=16t
4t^2-796t+380256=0
t=79.65 days Answer. Quadratic equation. [t=119.35 is extraneous]
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Ed
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graph%28500%2C500%2C-10%2C140%2C-100%2C600%2C4x%2B%288%2Asqrt%28x%29%29%2B110%29
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-796x%2B38025+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-796%29%5E2-4%2A4%2A38025=25216.

Discriminant d=25216 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--796%2B-sqrt%28+25216+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-796%29%2Bsqrt%28+25216+%29%29%2F2%5C4+=+119.349433241279
x%5B2%5D+=+%28-%28-796%29-sqrt%28+25216+%29%29%2F2%5C4+=+79.6505667587208

Quadratic expression 4x%5E2%2B-796x%2B38025 can be factored:
4x%5E2%2B-796x%2B38025+=+4%28x-119.349433241279%29%2A%28x-79.6505667587208%29
Again, the answer is: 119.349433241279, 79.6505667587208. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-796%2Ax%2B38025+%29