Answer
See the explanation below.
Work Step by Step
Given: $y(0)=1147$
when the population continues to decline at 39% per year, then we have
$y(20)= 1147 (1-0.39)^{20} \\ \implies y(20) \approx 0.06$
Thus, $y(20) \lt 1$
Hence, the species will be extinct.