Last September, I adopted a dog from our local pet shelter,Percy. Percy’s diet at the pet shelter was lacking to say the leastand, despite already being skin and bones, he was losing weight.After adopting Percy, it took a little while for him to acclimateto regular dog food and so he continued to lose weight, but at aslower rate. After about a month, Percy finally began to startgaining weight. Over the next two months, the rate at which he wasgaining weight was increasing. During our visit to the vet inDecember, our vet suggested that I may have gone overboard and lethim eat too much. She advised that I should reduce the amount Ifeed Percy and take him on more routine walks. During the month ofDecember, Percy’s weight gain tapered off, and starting in January,he actually began to lose weight. In February the vet was happywith his weight. I followed her recommendation to increase his foodslowly, and Percy’s weight loss slowed over the month. During thesefirst couple weeks of March, Percy’s weight actually seems to havestabilized at a healthy weight of 42lbs!

My professor was very excited to see me sign up to present andthought the project was a good idea. When I proposed it, myprofessor recommended that I should determine the followinginformation 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 isdecreasing.

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.