Please help asap

We want to find where  p(t)    =  0    [  no population  remains  ] 

So

0  = -t^4  + 72t^2  + 225     multiply through  by  -1  and rearrange

t^4 - 72t^2  - 225   = 0       this will factor as

(t^2  - 75) (t^2  + 3)  = 0

When set to  0  and solved for t, the second factor produces a non-real answer

For...the first factor we have

t^2  - 75  =0      add 75 to both sides

t^2   =  75   take the positive root

t ≈   8.66 years