you began membership in a new health and fitness club which has access to a dietician and personal trainer…

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.\n|time (weeks)|0|1|2|3|4|5|6|7|8|\n|weight (lb)|150|144|143|141|140|137|137|132|129|\nif 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?\n a. +0.38 pounds per week\n b. -0.38 pounds per week\n c. +2.6 pounds per week\n d. -2.6 pounds per week

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.\n|time (weeks)|0|1|2|3|4|5|6|7|8|\n|weight (lb)|150|144|143|141|140|137|137|132|129|\nif 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?\n a. +0.38 pounds per week\n b. -0.38 pounds per week\n c. +2.6 pounds per week\n d. -2.6 pounds per week

Answer

Explanation:

Step1: Identify the formula for average rate of change

The formula for the average rate of change of a function $y = f(x)$ over the interval $[x_1,x_2]$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here, the function is weight $w$ as a function of time $t$, and we want to find the average rate of change over the first five - week period. Let $t_1 = 0$ and $t_2=5$, $w(t_1)=150$ and $w(t_2)=137$.

Step2: Calculate the average rate of change

The average rate of change of weight with respect to time is $\frac{w(5)-w(0)}{5 - 0}$. Substitute $w(0)=150$ and $w(5)=137$ into the formula: $\frac{137 - 150}{5}=\frac{- 13}{5}=-2.6$ pounds per week.

Answer:

d. -2.6 pounds per week