Exploring Baby Weight Mathematically

A baby's weight changes dramatically in the first weeks of life. For example, let's look at data for Baby Kevin and Baby David.

Baby Kevin:
TIME birth 2 weeks 8.5 weeks 17 weeks 26 weeks
WEIGHT 7 lb, 6 oz 7 lb, 6 oz 11 lb, 7 oz 14 lb, 8 oz 16 lb, 5 oz

Baby David:
TIME birth 3 weeks 4 weeks 5 weeks
WEIGHT 7 lb, 9 oz 8 lb, 14 oz 9 lb, 12 oz 10 lb, 6 oz

The weight, K, of Baby Kevin in the xth week of his life is given by the model below in red.
Similarly, the weight D of Baby David in the xth week of his life is modeled by the equation in blue.

   

1. Graph the equation which models David’s weight using a graphing calculator and predict how much he will weigh at 6 weeks. Compare this to his actual weight, which I will tell you separately. (Sorry, I cannot report it to you here lest it spoil the discovery.) Do you think this model would be useful to predict David’s weight at 26 weeks? Why or why not?

 2.  Both models suggest that the boys weighed less than their birth weight at one time, which is true of almost all babies.  How long did it take Baby Kevin to return to his birth weight?  No equation is needed to answer this. However, you can’t easily answer the same question for Baby David without one. Use the model and a graphing calculator to approximate the day David again weighed 7 lb. 9 oz.  If you don't have a grapher, you still can find the answer by solving with pencil and paper. It may look formidable at first, but it can actually be done. How?

3. The model for Kevin’s weight is made of two equations: one piece for weeks 0 through 8.5, and another for weeks 8.5 through 26. Why was it constructed this way? Hint: A graphing calculator will unveil the answer.

4. What amount does the model suggest is the smallest David ever weighed? How old was he at  this time? Same questions for Kevin.

5.  At what age do you think the boys were closest in weight? Was it at birth (3 oz.)? Was it at the age David weighed his lowest? After you take a guess, use a graphing calculator to determine what the model suggests.

Want to know how to find the answers to these and other interesting questions? 
Take my College Algebra class MA 153 or MA 151 and you're on your way!


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Last updated: August 13, 2001
URL: http://www.ipfw.edu/math/lamaster/baby2/babyweqn.htm
Contact: John LaMaster, Instructor, (219) 481-5430
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