Rabbit population - how do I know which equation?? I have attached an image of the question, #40. 

I'm struggling with part A because I'm not sure if I have the following equation right. 
$\frac{dR}{dt} = Ce^{0.12 t} + 300$
Or is it 
$\frac{dR}{dt} = 0.12R(1-\frac{P}{300})$?
Any help is appreciated. Thank you.
 A: Without the wolves, you would have something like $\frac{dP}{dt}=0.12P(t)$. If you solve this differential equation, you'll get $P(t)=Ce^{0.12t}$, which is the form you're probably more used to. In general, an exponential function $f(x)=Ce^{ax}$ satisfies the differential equation $f'(x)=af(x)$. In fact, the exponential function can be defined as the solution to this equation.
The "300 rabbits" bit comes into play when you try to find the constant $C$. $P(t)=Ce^{0.12t}$ defines a family of solutions, each parametrized by a unique value of $C$. (This is true in general for solutions of differential equations.) To find the solution you want, you use the fact that $P(0)=300$. However, $C$ doesn't show up in the original differential equation, so you don't need that information to solve part a).
You also need to consider the wolves. If you include them, you get $\frac{dP}{dt}=0.12P(t)-rH(t)$, where $H$ is the Heaviside function. Heaviside functions are useful for describing behavior that changes abruptly at a certain point. In this case, the wolves begin eating rabbits at $t=0$, so we need an equation that will change abruptly to reflect this.
