Question

The table below shows the distance d(t) in feet that an object travels in t seconds: t (seconds) d(t) (feet) 1 15 2 60 3 135 4 240 What is the average rate of change of d(t) between 2 seconds and 4 seconds, and what does it represent?

50 ft/s; it represents the average speed of the object between 2 seconds and 4 seconds
90 ft/s; it represents the average speed of the object between 2 seconds and 4 seconds
90 ft/s; it represents the average distance traveled by the object between 2 seconds and 4 seconds
50 ft/s; it represents the average distance traveled by the object between 2 seconds and 6 seconds

Answer 1

Answer:the correct answer is Option B

Explanation:

90 ft/s; it represents the average speed of the object between 2 seconds and 4 seconds

Answer 2

Explanation:

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.

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).

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 ;

=

Simplify:

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.