Exponential Growth and Decay指数增长和衰变

1、.Exponential Growth and DecayExponential growth and decay occurs when quantities increase or decrease proportional to the quantity present.Ex.GrowthDecaySavings AccountsRadioactive ChemicalsRRSPsCarbon DatingBacterial CulturesValue of a vehiclePopulation GrowthConsider a city thats population grows

2、at 5% per year. In the year 2000 the population was 100 000.2001100 000 x 1.05 = 105 0002002105 000 x 1.05 = 1102502003110 250 x 1.05 = 115 763n-yearsThe function that expresses the population after n years is .Ex.A vase was purchased in 1990 for $8000. If the vase appreciates at 6% per year, how mu

3、ch:a. Was it worth in the year 2000.b. Will it be worth in the year 2030.The standard form of an exponential growth or decay is . is the initial amount.b is the growth (1 + i) or decay (1- i) factori is the percent rate of growth or decay (as a decimal).t is the number of growth or decay periods (th

4、is depends on the question)Ex.The world population doubles every 35 years. If the population was 6 billion in 1999, find:a. The population in 2050.b. When the population will be 24 billion.Sometimes, you will be asked to find the rate of increase of a population. Ex.The population of a town was 2400

5、0 in 1980, and 29000 in 1990.a. Determine an expression to find the population in t years after 1980.b. What will be the population in 2020?Exponential DecayEx.A car depreciates by 15% per year. If you buy a car for $15 000, find the value of the car in . a)3 yearsb) 10 yearsHalf-LifeEx.An isotope of radium has a half-life of 1620 years. If you have 10mg, how much w