Question

You began membership in a new health and fitness club which has access to a dietician and personal trainer. They help you develop a special eight-week diet and exercise program. The data in the following table represents your weight, w, as a function of time, t, over an eight-week period.
Time (weeks)
0
1
2
3
4
5
6
7
8
Weight (lb)
150
144
143
141
140
137
137
132
129

During which time period is the average rate of change zero?
a.
From week 7 to week 8
b.
From week 3 to week 4
c.
From week 0 to week 1
d.
From week 5 to week 6

Answer 1

I think it's 5 to 6 but that's just my guess.

Answer 2

Answer:

The correct option is d.

Step-by-step explanation:

The average rate of change of a function between two points is defined as

$m=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

If during a time period the average rate of change is zero, then

$0=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

$0=f(x_2)-f(x_1)$

It means the value of the function is same for both the points.

From the given table it is clear that the weight is same for 5th and 6th week.

$m=\frac{f(6)-f(5)}{6-5}$

$m=\frac{137-137}{1}$

$m=0$

So, the average rate of change zero from week 5 to week 6.

Therefore the correct option is d.