4.2+Fighting+Fleas

SO **January 13, 2009** **Essential Question: //How can I show a problem of repeated division?//** 
 * Big Idea: //The rate at which many things grow or decay can often be described mathematically.//**

It decreases by half the amount each hour the medicine is in the dog.
 * A. How does the amount of active medicine in the dog's blood change from one hour to the next?**

m=20(.5n)
 * B. Write an equation to model the relationship between the number of hours since the dose as administered, b, and the milligrams of active medicine, m.**

I don't expect to see a change because half of 40 milligrams is 20 and that is where the original dose started.
 * C. Based on your knowledge of exponential relationships, what pattern would you expect to see in the data if 40 milligramsof the medicine were given to the dog?**


 * FOLLOW UP

1. Suppose that after an initial dose of 60 milligrams, a flea medicine breaks down at a rate of 20% per hour in an animal's bloodestream. This means that as each our passes, 20% of the active medicine is used. Copy and complete the table to show the amount of active medicine in an animal's blood at the end of each hour for 6 hours.2**
 * Time Since Dose (hours) || Active Medicine In Blood (milligrams) ||
 * 0 || 60 ||
 * 1 || 48 ||
 * 2 || 38.4 ||
 * 3 || 30.72 ||
 * 4 || 24.576 ||
 * 5 || 19.661 ||
 * 6 || 15.729 ||

** 2. For the medicine described in   question 1, Janelle wrote the equation m=60(.08b) to model the relationship between the amount of medicine in the blood and the number of hours since it was administered. Compare the quantities of active medicine in your table to the quantities given by Janelle's equation for several time values. Explain any similarities or differences you find. **Both data sets will end up the same because taking away 20% is the same as multiplying .8. This is because .8= 80% and when you take away 20% from 100% you are left with 80%.

When you have 100% and you take away 20% you are left with 80%. So 20% less than 100% is 80%. So for example with 60 you are trying to find 20% less than 60, or 80//**%**// __of__ 60. Of means multiply so you need to multiply .8 and not .2.
 * 3.Janelle's friendHabib was confused by the terms rate of decay and decay factor. He said that since the rate of decay in question 1 is 20%, the decay factor should be .2 and the equation should be m=60(0.2h). How would you explain to Habib why a rate of decay of 20% is equivalent to a decay factor of 0.8**?