To estimate the average rate of change of the function \( f(x) = 1.6875x \) between \( x = 3.9 \) seconds and \( x = 8.2 \) seconds, we can use the formula for average rate of change:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
where \( a = 3.9 \) and \( b = 8.2 \).
First, calculate \( f(3.9) \):
\[ f(3.9) = 1.6875 \times 3.9 = 6.57875 \]
Next, calculate \( f(8.2) \):
\[ f(8.2) = 1.6875 \times 8.2 = 13.8375 \]
Now, substitute these values into the average rate of change formula:
\[ \text{Average Rate of Change} = \frac{13.8375 - 6.57875}{8.2 - 3.9} \]
Calculate the difference in function values:
\[ 13.8375 - 6.57875 = 7.25875 \]
Calculate the difference in time:
\[ 8.2 - 3.9 = 4.3 \]
Now, substitute these into the formula:
\[ \text{Average Rate of Change} = \frac{7.25875}{4.3} \approx 1.69 \]
Therefore, the average rate of change between 3.9 seconds and 8.2 seconds is approximately 1.69 feet/second.
The correct response is:
about 1.69 feet/second.