SOLUTION: A large pond is stocked with fish.The fish population P is modeled by the formula:P=3t+10t^1/2+140, where t is the number of days since the fish were first introduced into the pon

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Question 418067: A large pond is stocked with fish.The fish population P is modeled by the formula:P=3t+10t^1/2+140, 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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A large pond is stocked with fish. The fish population P is modeled by the formula:P=3t+10t^1/2+140,
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?
:
Write the equation:
3t + 10t^1/2 + 140 = 500
:
Subtract 140 from both sides
3t + 10t^1/2 = 500 - 140
3t + 10t^1/2 = 360
;
We can write this as
3t+%2B+10sqrt%28t%29+=+360+
10sqrt%28t%29+=+360+-+3t+
;
square both sides
100t+=+%28360-3t%29%5E2
100t+=+129600+-+1080t+-+1080t+%2B+9t%5E2
;
Arrange as a quadratic equation
9t^2 - 2160t - 100t + 129600 = 0
9t^2 - 2260t + 129600 = 0
:
A tiresome equation, use the quadratic formula; a=9, b=-2260, c=129600
Two solutions, only one is valid
t = 88.62 days to reach 500 fish
;
:
Check this in the original equation
P = 3t + 10t^1/2 + 140
P = 3(88.62) + 10(88.62^1/2) + 140
P = 265.86 + 10(9.414) + 140
P = 265.86 + 94.14 + 140
P ~ 500 fish