you begin membership in a new health and fitn...
you begin 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 if you lost 13 pounds in the first five weeks, what is the average rate of change of weight with respect to time over the first five weeks of the program? a. +0.38 pounds per week b. -0.38 pounds per week c. +2.6 pounds per week d. -2.6 pounds per week please select the best answer from the choices provided
Answer
# Answer:
D. -2.6 pounds per week
# Explanation:
## Step1: Recall rate - of - change formula
The average rate of change formula is $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$, where $y$ is the weight and $x$ is the time.
## Step2: Identify values
Here, the change in weight $\Delta y=- 13$ pounds (negative because weight is lost), and the change in time $\Delta x = 5-0 = 5$ weeks.
## Step3: Calculate average rate of change
$\frac{\Delta y}{\Delta x}=\frac{-13}{5}=-2.6$ pounds per week.