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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

The number N(t) of new cases of a flu outbreak for a given city is given by N(t) = 6500 * 2^(-0.03t^2), where t is the number of months since the outbreak began. (a) Find the average rate of change in the number of new flu cases between months 0 and 2, and interpret the result. (b) Find the average rate of change in the number of new flu cases between months 4 and 6, and between months 10 and 12. (c) Use a graphing utility to graph the function and use the graph and the average rates of change to discuss the pattern of the number of new flu cases.

Find the average rate of change in the number of new flu cases using the function N(t) = 6500 * 2^(-0.03t^2). This problem involves exponential functions, calculating the average rate of change over specific intervals, and interpreting the results with a graphing utility. Suitable for students in Grades 10-12.

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