Unit 8 A Growth Linear versus Exponential Ms

Unit 8 A Growth: Linear versus Exponential Ms. Young Slide 8 -1

8 -A Growth: Linear versus Exponential § Linear Growth occurs when a quantity grows by some fixed absolute amount in each unit of time. § Exponential Growth occurs when a quantity grows by the same fixed relative amount— that is, by the same percentage—in each unit of time. Ms. Young Slide 8 -2

8 -A Growth: Linear versus Exponential Straightown grows by the same absolute amount each year and Powertown grows by the same relative amount each year. Ms. Young Slide 8 -3

8 -A Key Facts about Exponential Growth § Exponential growth leads to repeated doublings. With each doubling, the amount of increase is approximately equal to the sum of all preceding doublings. § Exponential growth cannot continue indefinitely. After only a relatively small number of doublings, exponentially growing quantities reach impossible proportions. Ms. Young Slide 8 -4

8 -A Example Bacteria in a Bottle: Suppose you put a single bacterium in a bottle at 11: 00 a. m. It grows and at 11: 01, it divides into two bacteria. These two bacteria grow and at 11: 02 divide into four bacteria, which grow and at 11: 03 divide into eight bacteria, and so on. Thus, the bacteria doubles every minute. If the bottle is half-full at 11: 59, when will the bottle be completely full? Since the bacteria doubles every minute, the bottle will be full after one more minute. That is, the bottle will be completely full at 12: 00 p. m. Ms. Young Slide 8 -5