Exponential Population Growth ·Examples of this? Think close to home Often an unnatural occurrence Conditions under which this occurs naturally Invasive species -Nutritionally enriched environments Cultural innovations? 11
11 Exponential Population Growth • Examples of this? – Think close to home • Often an unnatural occurrence • Conditions under which this occurs naturally – Invasive species – Nutritionally enriched environments – Cultural innovations?
Bacterial(细菌)growth Time Number of Cells 70 0 minutes 1 =20 60 20 2 =21 40 4 =22 50 60 8 =23 80 16 -24 40 100 32 =25 30 120(=2 hours) 64 =26 =29 20 3 hours 512 G=rN 4 hours 4,096 =212 10 8 hours 16,777,216 =224 20406080100120140 12 hours 68,719,476,736=236 Time(min) Figure 35.3A 12
12 Figure 35.3A Bacterial (细菌) growth
Example problem The human population of the earth is growing at approximately 1.8%per year. The population at the start of 2001 was approximately 6 billion. If nothing were to slow the rate of population growth,what would the population be in the year 2101? 13
13 Example problem • The human population of the earth is growing at approximately 1.8%per year. • The population at the start of 2001 was approximately 6 billion. • If nothing were to slow the rate of population growth, what would the population be in the year 2101?
Answer ·N(t)=Net 。r=.018 ·t=100 years ·No=6 billion ·N(100)=Noet ·N(100)=6x109et=6x109*e1.8 ·N(100)=6x109*6.04=36.3 billion 14
14 Answer • N(t)=N0ert • r= .018 • t=100 years • N0=6 billion • N(100)=N0ert • N(100)=6x109ert =6x109*e1.8 • N(100)= 6x109*6.04 = 36.3 billion
例：根据模型求人口增长率和人口加倍时间 如：1949年我国人口5.4亿，1978年为9.5 亿，求29年来人口自然增长率和周期增长率 入；若按照这种速度，人口加倍的时间是多少 年？ 1 10 ◆11.4 本9.58 86 ◆4. +.48 2 ◆*2.0丽 0 ◆0.8 1578 1678 1778 1878 1978 年（公元） ◆-人口（亿） 15
15 例：根据模型求人口增长率和人口加倍时间 如：1949年我国人口5.4亿，1978年为9.5 亿，求29年来人口自然增长率 r和周期增长率 λ；若按照这种速度，人口加倍的时间是多少 年？