Problem:Dr. David Smith, a math professor at Duke University, had a golden retriever named Sassafras.When Sassy was a puppy, Dr. Smith recorded her weight at ten day intervals:

Birth (10/24/89) 3.25 pounds

10 days 4.25 pounds

20 days 5.5 pounds

30 days 7 pounds

40 days 9 pounds

50 days 11.5 pounds

60 days 15 pounds

70 days 19 pounds

At the time when Dr. Smith finished collecting this data, Sassy was getting cup of food three times a day but the plan was to change this to 1 cup of food twice a day when Sassy reached 30 pounds. Dr. Smith wanted to know if Sassy will have reached this weight when she was 80 days old.If not, then he wanted to know when she would reach 30 pounds. We will make the prediction ourselves after modeling the above data. Answer all of the questions on the following pages.

Develop a Mathematical Model: Working together in small groups, look for patterns in the data and design a process to predict Sassy's weight from her age. Discuss as a group and make sure that you all agree on the modeling process. Then explain your process in detail.Do not use a graph for this part of the activity.

Mathematically Speaking: Answer the following questions about your mathematical model:

Represent your mathematical model symbolically.

Provide numerical support for why this is the best mathematical model that you could find. How accurate are its predictions for Sassy's weight at ages where Dr. Smith has already measured her weight?

Describe how the rate of change of your mathematical model behaves.

Describe how the percent change of your mathematical model behaves.

Is your model linear? If so, find the slope and-intercept of your model and explain their meaning in practical terms for this particular situation.

Is your model exponential? If so, find the initial value and percent change of your model and explain their meaning in practical terms for this particular situation.

Visualize the accuracy of your model by plotting your data andyour modeling functiontogether on the same set of axes.Does your model appear to accurately represent the trend of the data? If it doesn't revise your model and redo the questions above before continuing.

Make a Prediction: Using the modeling process that you have developed, predict Sassy's weight when she is 80 days old. Has Sassy reached 30 pounds after 80 days?

Solution to Dr. Smith's Problem: How old will Sassy be when she reaches 30 pounds? (Notice you can answer this question numerically or graphically if you are unable to do so symbolically.)