The population of a species is modeled by the equation p(t) = -t^4+72t^2+225 where t is the number of years. Find the approximate number of years until the species is extinct.
Set it to zero and solve.
Do you need help or do you have it?
I got it
Nice!
you would get two answers?
which is t=+/- 5 radical 3 and t= +/- radical 3i?
you should be interested only in **real** solutions for t, one of which is negative ..... so time travel limits that one !!
assume you re-wrote it as \(t^2 = \tau\) and so: \(p(\tau) = -\tau^2+72\tau+225\) ....and solved from there \(\implies \tau = - 3 , 75\) whence: \(t = \dots\)
but with physical (real life) applications you must also use common-sense :) so the imaginary solutions are meaningless, as is the notion of -ve time
how did you get -r^2+72r+225 the equation is -t^4+72t^2+225
solve it as a quadratic.
\(p(t) = -t^4+72t^2+225\) \(p(\tau) = -\tau^2+72\tau+225\) where: \(\tau = t^2\) solve for \(\tau\), then for \(t\)
did you solve it another way?
when you solve using quadratic formula you would get -7 +/- 6 radical 119 all over -2
\(p(\tau) = -\tau^2+72\tau+225\) \(\tau_{1,2} = \dfrac{- 72 \pm \sqrt{(72)^2 - 4 (-1)(225)}}{2(-1)} = -3, 75\)
thusly: because \(\tau = t^2\) we have: \(t_{1.,2} = \sqrt {\tau }= \sqrt{-3}, \sqrt{75}\)
yes
wouldn't radical -3 be 3i
\(\sqrt{-3} = \sqrt{3}\sqrt{-1} = \sqrt{3} ~ i\)
because \(i = \sqrt{-1}\)
and that after that what did you do to get your answer?
the answer is the positive real solution, ie \(\sqrt{75} = \sqrt{3 \times 5^2} = 5 \sqrt 3\) you got that answer, but you got 3 other answers too. i've prolly confused you, but you have to see through the mist.
ok
then what do u do?
that's it
you can type \(\sqrt 3\) into yer calculator, i suppose and turn the answer into \(5 \sqrt 3 \approx 8.66\)
here's a sketch of the function: |dw:1513299732076:dw|
tmi, maybe. :(
thank you!
mp!
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