# Fish population problem.

• Feb 1st 2009, 01:33 PM
tmac11522
Fish population problem.
A large pond is stocked with fish. The fish population P is modeled by the formula P = 3t + 10t + 120, 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?
• Feb 1st 2009, 02:02 PM
wytiaz
fish
Ok, so the population wanted is 500. We plug in and now we have:

500
= 3t + 10t + 120, solve for t

I suggest bringing the 3t and then 120 to the left side with subtraction then squaring both sides as your first few steps to solving for t.
• Feb 1st 2009, 02:08 PM
skeeter
Quote:

Originally Posted by tmac11522
A large pond is stocked with fish. The fish population P is modeled by the formula P = 3t + 10t + 120, 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?

$500 = 3t + 10\sqrt{t} + 120$

$0 = 3t + 10\sqrt{t} - 380$

let $u = \sqrt{t}$ ...

$0 = 3u^2 + 10u - 380$

$u = \frac{-10 \pm \sqrt{100 - 4(3)(-380)}}{6}$

taking the positive solution ...

$u \approx 9.7107$ ...

$t = u^2 \approx 94.3$ days