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(7569)   (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]
.
Ed
.
.
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=25216 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 119.349433241279, 79.6505667587208.
Here's your graph:
 |
|
|
|
