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
[tex]p(t)=-t^4+72t^2+225[/tex]
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
[tex]p(t)=-t^4+72t^2+225=0[/tex]
we can factor it
[tex](t^2+3)(t^2-75)=0[/tex]
[tex](t^2+3)=0[/tex]
we get t value as imaginary for this equation
[tex](t^2-75)=0[/tex]
[tex]t=\sqrt{75}[/tex]
[tex]t=8.660[/tex]
So,
the approximate number of years until the species is extinct will be 9 years
