Question

Last September, I adopted a dog from our local pet shelter, Percy. Percy’s diet at the pet shelter was lacking to say the least and, despite already being skin and bones, he was losing weight. After adopting Percy, it took a little while for him to acclimate to regular dog food and so he continued to lose weight, but at a slower rate. After about a month, Percy finally began to start gaining weight. Over the next two months, the rate at which he was gaining weight was increasing. During our visit to the vet in December, our vet suggested that I may have gone overboard and let him eat too much. She advised that I should reduce the amount I feed Percy and take him on more routine walks. During the month of December, Percy’s weight gain tapered off, and starting in January, he actually began to lose weight. In February the vet was happy with his weight. I followed her recommendation to increase his food slowly, and Percy’s weight loss slowed over the month. During these first couple weeks of March, Percy’s weight actually seems to have stabilized at a healthy weight of 42lbs!

My professor was very excited to see me sign up to present and thought the project was a good idea. When I proposed it, my professor recommended that I should determine the following information to help me graph Percy’s weight as a function

1. Define what corresponds to t=0

2. Find where f'(t) is positive and where it is negative.

3. Find where f'(t) is increasing and where it is decreasing.

Unfortunately, I am having trouble getting started with this. Please explain how to figure out (1), (2) and (3) above. Finally, give a graph of my dog’s weight and explain how you used (2) and (3) to get this graph. I’ll need to define what the axes represent, so be sure to tell me what choices you make for this.

Answer 1

Solution:

Given that,

   Percy’s diet at the pet shelter was lacking to say the least .

   Despite already being skin and bones, he was losing weight.

  Percy finally began to start gaining weight. Over the next two months, the rate at which he was gaining weight was increasing.