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

The correct option is d.

Explanation:

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

`m=(f(x_2)-f(x_1))/(x_2-x_1)`

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

`0=(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=(f(6)-f(5))/(6-5)`

`m=(137-137)/(1)`

`m=0`

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

Therefore the correct option is d.