[填空题]
A small population of ra +w-boro5kxbk9 mx1/a bbits in a0 d0eii2c4+ph tzmf6a forest is observed. After t weeks the population is modet0a zp6 dhc40i+em2f illed 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.
