[填空题]
A small population of rabbits ik2j zdo3 2(c an)gcdv*0 qaaild.c;9wn a forest is observed. ;xltle-e4pms 52yg-o After t weeks the population is modep 2 x yemo5;l4t-ls-gelled 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.
