Questions: The graph gives the weight W of a person at age x. (a) Determine the intervals on which the function W is increasing. (Select all that apply.) (0,30) (0,40) (30,32) (30,40) (32,68) Determine the intervals on which the function W is decreasing. (Select all that apply.) (0,30) (0,40) (30,32) (30,40) (32,68) (b) What do you think happened when this person was 30 years old? This answer has not been graded yet (c) Find the net change (in lb) in the person's weight W from age 10 to age 50. lb

Solution Steps

The function $W$ is increasing when the graph goes upwards when reading from left to right. The intervals where the function is increasing are $(0, 30)$, $(32, 40)$, and $(32, 68)$. Notice that the interval $(0, 40)$ is incorrect as there is a period within that interval where the function is decreasing. Also, note that between ages $30$ and $32$, the function is decreasing, so $(30, 32)$ is not a valid interval. Therefore, only $(0, 30)$, $(30,40)$ and $(32, 68)$ are valid intervals.

The function $W$ is decreasing when the graph goes downwards when reading from left to right. Looking at the graph, the only decreasing portion is between $x=30$ and $x=32$. Therefore, the interval where the function is decreasing is $(30, 32)$.

The weight at age $30$ is about $150$ lb, which decreases to about $140$ lb by age $32$, before increasing again. It is possible that the person experienced an illness or changed their lifestyle in some way that led to the decrease in weight around age 30.

Final Answer: