Part 1 of 2 Write an exponential decay function to model the situation. Compare the average rates of change over the given intervals. initial value: 49 decay factor: 0.8 \( 1 \leq x \leq 3 \) and \( 4 \leq x \leq 8 \) The exponential decay function to model the situation is \( \mathrm{f}(\mathrm{x})=\square \).

The exponential decay function to model this situation is \( f(x) = 49 \cdot (0.8)^x \). This function starts at 49 when \( x = 0 \) and decreases by a factor of 0.8 for each increment of \( x \). To compare the average rates of change over the intervals \( 1 \leq x \leq 3 \) and \( 4 \leq x \leq 8 \), simply compute the function values \( f(1), f(3), f(4), \) and \( f(8) \), then use the formula \( \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \) for each interval. This will show how quickly the values are decreasing in each time span!