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.

Answer 1

Answer:

The approximate number of years until the species is extinct will be 9 years

Step-by-step explanation:

We are given

The population of a species is modeled by the equation

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

where

t is the number of years

we have to find time when species extinct

we know that any species will be extinct only if population of that species becomes 0

so, we can set P(t)=0

and then we can solve for t

$p(t)=-t^4+72t^2+225=0$

we can factor it

$(t^2+3)(t^2-75)=0$

$(t^2+3)=0$

we get t value as imaginary for this equation

$(t^2-75)=0$

$t=\sqrt{75}$

$t=8.660$

So,

the approximate number of years until the species is extinct will be 9 years