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.

Question

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.

Shadow · Answer

Set it to zero and solve.

Shadow · Answer

Do you need help or do you have it?

candygirl220 · Answer

I got it

Shadow · Answer

Nice!

candygirl220 · Answer

you would get two answers?

candygirl220 · Answer

which is t=+/- 5 radical 3 and t= +/- radical 3i?

sillybilly123 · Answer

you should be interested only in **real** solutions for t, one of which is negative ..... so time travel limits that one !!

sillybilly123 · Answer

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: $t = \dots$

sillybilly123 · Answer

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

candygirl220 · Answer

how did you get -r^2+72r+225

the equation is -t^4+72t^2+225

sillybilly123 · Answer

solve it as a quadratic.

sillybilly123 · Answer

$p(t) = -t^4+72t^2+225$

$p(\tau) = -\tau^2+72\tau+225$

where: $\tau = t^2$

solve for $\tau$, then for $t$

sillybilly123 · Answer

did you solve it another way?

candygirl220 · Answer

when you solve using quadratic formula you would get -7 +/- 6 radical 119 all over -2

sillybilly123 · Answer

$p(\tau) = -\tau^2+72\tau+225$

$\tau_{1,2} = \dfrac{- 72 \pm \sqrt{(72)^2 - 4 (-1)(225)}}{2(-1)} = -3, 75$

sillybilly123 · Answer

thusly:

because $\tau = t^2$ we have:

$t_{1.,2} = \sqrt {\tau }= \sqrt{-3}, \sqrt{75}$

candygirl220 · Answer

yes

candygirl220 · Answer

wouldn't radical -3 be 3i

sillybilly123 · Answer

$\sqrt{-3} = \sqrt{3}\sqrt{-1} = \sqrt{3} ~ i$

sillybilly123 · Answer

because $i = \sqrt{-1}$

candygirl220 · Answer

and that after that what did you do to get your answer?

sillybilly123 · 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.

candygirl220 · Answer

ok

candygirl220 · Answer

then what do u do?

sillybilly123 · Answer

that's it

sillybilly123 · Answer

you can type $\sqrt 3$ into yer calculator, i suppose and turn the answer into $5 \sqrt 3 \approx 8.66$

sillybilly123 · Answer

here's a sketch of the function:
|dw:1513299732076:dw|

sillybilly123 · Answer

tmi, maybe.  :(

candygirl220 · Answer

thank you!

sillybilly123 · Answer

mp!