Question

How fast is the size of the population changing after 1 minute? 

Answer 1

$$P(t)=3t^2+3e^t+10, t\geq0$$

$$P'(t)=(3t^2+3e^t+10)'=6t+3e^t$$

Given $t=1\ min=60\ sec.$

$$P'(60)=6(60)+3e^{60}=360+e^{60}\approx1.142\times10^{26}$$

The popukation increases at rate of $360+e^{60}\approx1.142\times10^{26}$ bacteria per second after 1 minute.