The function provided is $N(t) = 6500 \cdot 2^{-0.03t^2}$, where $N(t)$ is the number of new flu cases and $t$ is the number of months since the outbreak began. Let's work through each part of the problem step by step.

Part (a): Average Rate of Change Between Months 0 and 2

The average rate of change of a function between two points is calculated using the formula:

$\text{Average Rate of Change} = \frac{N(t_2) - N(t_1)}{t_2 - t_1}$

For months $t_1 = 0$ and $t_2 = 2$:

1. Calculate $N(0)$ and $N(2)$: [ N(0) = 6500 \cdot 2