Consider a population of organisms undergoing exponential growth. The population size $($

$$

N$)$ can be modeled by the equation

$$

$($

$$

$)$

$=$

$$

$0$

$\backslash$times

$$

$$

$$

N$($t$)=$N

$0$

$$

$\backslash$times e

rt

$,$ where

$$

$0$

N

$0$

$$

is the initial population size,

$$

r is the growth rate, and

$$

t is time.

Now, introduce a predator$-$prey interaction into the system, modeling it using the Lotka$-$Volterra equations: