2.3+Growing+Mold

 Big Idea The rate at which many things grow or decay can often be described mathematically. Essential Question  - What does the growth of mold have to do with Math? **NOTES ****- discussion on growth factor. ** **__Vocabulary __** Growth factor - the constant factor that each value in an exponential growth pattern is multiplied by to get the next value.  Try this - take out one piece of bread and pat it with your hands. Put the piece of bread into a zip-lock bag. Leave it on the counter. Wash your hands thoroughly and with another piece of bread, pat your hands on it. Put it in a zip-lock bag and leave it on the counter. Over week observe how the two pieces of bread are different.
 * __ Sidratun M.  __** **__  12.07.08  __** **__  Block-8D  __**

**__  2.3 Growing Mole   __** A.   ****  Describe how the mold area changes from one day to the next. ** Each day the mold is multiplied thrice. So every new day the mold increases 3 times more from the previous day. This is an exponential relationship. B.   ****  Write an equation for the mold area, A after d days. ** A=3^D C.   ****  How is your answer to part A reflected in your equation? ** Since the area is tripled everyday, 3 is the growth factor in the equation. The exponent is the number of day. So we multiply 3 //D// number of times to find the area. 
 * Look at the pattern in the (day, mold area) data. **
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 * __ Problem 2.3 Follow-Up __ **
 * Suppose that on day 0, a patch of bread mold has an area of 25 mm^2(one fourth of a square centimeter) and that the mold grows in the same exponential way it did in problem 2.3**
 * 1. Copy and complete the table to show the growth of the mold area.**
 * DAY || MOLD AREA (mm^2) ||
 * 0(start) || 25 ||
 * 1 || 75 ||
 * 2 || 225 ||
 * 3 || 675 ||
 * 4 || 2025 ||

**2. Write an equation for the mold area, //A//, after //d// days.** A=25 x 3^D 25 indicates the starting value and 3^D indicates the change from one day to the next. A. 2 B. 2 C. 3 **D. the growth of bread mold.** D. 3 50 3  12150 mm^2 The mold reached 10 cm^2 on the 3rd day.
 * 3. Which part of your equation indicates the starting value? Which part indicates the change from one day to the next?**
 * 4. Give growth factors for each situation.**
 * A. making ballots by repeatedly cutting stacks of paper in half**
 * B. reward plan 1**
 * C. reward plan 2**
 * 5. Ilan’s biology class did an experiment with the bread mold. They wrote the equation A=50(3^D) to represent the area in mm^2 of the mold after d days.**
 * A. what was the area for the patch of the mold at the start of the experiment?**
 * B. What was the growth factor?**
 * C. What was the area of the mold after 5 days?**
 * D. on which day did the area of the mold reach 10 cm^2?**