Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.5 - Equations - 1.5 Exercises - Page 58: 134

Answer

The fish population will reach 500 after 89 days.

Work Step by Step

$P=3t+10\sqrt t+140$ $P=500$, find t $500=3t+10\sqrt t+140$ $3t+10\sqrt t-360=0$ Let $a=\sqrt t$, a>0 then $3a^{2}+10a-360=0$ $a=\frac{-10+\sqrt (10^{2}-4\times3\times(-360))}{2\times3}=\frac{-10+\sqrt 4420}{6}=9.41$ or $a=\frac{-10-\sqrt (10^{2}-4\times3\times(-360))}{2\times3}=\frac{-10-\sqrt 4420}{6}=-12.75$(eject) $a=9.41$, then $\sqrt t=9.41$, so $t=9.41^{2}=88.5481\approx89$days So the fish population will reach 500 after 89 days
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