Population Model Initial Value Problem

The number of insects in a population is modeled by a differentiable function $P$, where $t$ is the time in days. The rate of change of the population is given by $P'(t) = 0.3t^2 + 12t + 210$. Given the initial condition $P(0) = 40$, which of the following statements are true?

I. At time $t = 10$, the population consists of 2840 insects.

II. At time $t = 10$, the population is increasing at a rate of 360 insects per day.

III. At time $t = 10$, the rate of population growth is increasing by 18 insects per day per day.