Answer:
Option B is correct
The average rate of change of d(t) between 2 second and 4 second is; 90 ft/s
and it represents the average speed of the object between 2 seconds and 4 seconds.
Step-by-step explanation:
Average rate of change of function is defined as the ratio of the difference in the function f(x) as it changes from a to b to the difference between a and b. Then, the average rate of change is denoted as A(x).
\(A(x) =\frac{f(b)-f(a)}{b-a}\)
As per the given statement, the distance d(t) is in feet and t is the time in second.
To find the average rate of change of d(t) between 2 seconds and 4 seconds.
From the table we have;
at t = 2 , d(2) = 60
and
at t =4 , d(4) = 240.
Then, by the definition of average rate of change ;
\(A(t) = \frac{d(4)-d(2)}{4-2}\) = \(\frac{240-60}{4-2} =\frac{180}{2}\)
Simplify:
\(A(t) = 90 ft/s\)
therefore, the average rate of change of d(t) between 2 second and 4 second is; 90 ft/s and it represents the average speed of the object between 2 seconds and 4 seconds.
