Question

q 9. part 1
this question is calculator active.
the graph of f(t) models the height, in feet, that a bee is flying above the ground with respect to the time it has traveled in t seconds.
what is the rate of change of the bee’s height on the time interval ( 6 leq t < 10 )? be sure to include units.

Explanation:

Step1: Identify points on the graph

At \( t = 6 \) seconds, from the graph, the height \( f(6) \) is 6 feet. At \( t = 10 \) seconds, the height \( f(10) \) is 0 feet (since the graph reaches the height of 0 at \( t = 10 \)).

Step2: Use the rate of change formula

The rate of change (slope) between two points \( (t_1, f(t_1)) \) and \( (t_2, f(t_2)) \) is given by \( \frac{f(t_2)-f(t_1)}{t_2 - t_1} \). Here, \( t_1=6 \), \( f(t_1) = 6 \), \( t_2 = 10 \), \( f(t_2)=0 \). So we calculate \( \frac{0 - 6}{10 - 6}=\frac{-6}{4}=-\frac{3}{2}=- 1.5 \) feet per second.

Answer:

The rate of change is \(-1.5\) feet per second (or \(-\frac{3}{2}\) feet per second).