[填空题]
A small population of rabbits in a forest is observed. After t weeks th to5u, l+4digundmy 32e popula1w0kg5udk uxu 4l1x0ftion isu4wx1kx0 0 u 51lfkudg modelled by
$P(t)=\frac{15000}{1+50 e^{-0.6 t}}, \text { where } 0 \leq t \leq 30$.
1. Find $P^{\prime}(t)$=$\frac{ae^{-0.6t}}{\left(1+50 e^{-0.6 t}\right)^{2}}$. a= .
2. Find the rate at which the population is increasing after 10 weeks.$p^'(10)$≈ .
3. Determine the time(s) at which the population is increasing at 1860 rabbits per week. Round your answer(s) to the nearest integer.
4. During which week does the rate at which the population is increasing reach its maximum.
