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Warm Up: Find the final amount : Invest $4000 at 6% compounded quarterly for 20 years. r A P 1 n nt 0.06 A $40001 4 A $13,162.65 420 Invest $5600 at 3.7% compounded continuously for 12 years. A Pe rt 0.03712 A 5600e A $8,730.01 Application Problems Growth and Decay Growth P 1 r t Decay P 1 r t The population of Durango is 50,000. If it grows at a rate of 2%, what will the population be in one year? Growth P 1 r t Growth 50,0001 0.02 50,0001.02 $51,000 1 The population of Cedar Oak in 1920 was 6500. If the population is growing at a rate of 5% per year, what will the population be in 1970? Growth P 1 r t A 65001 0.05 A 74,538 50 The population of Walden in 1930 was 350,000. If the population is decreasing at a rate of 2.5% per year, what will the population be in 1990? Decay P 1 r t A 350,0001 0.025 A 76,621 60 The population of Greenwood in 1940 was 7400. If the population is growing at a rate of 4.5% per decade, what will the population be in 2010? Growth P 1 r t A 74001 0.045 70 10 A 74001.045 A 10,070 7 The population of Glenview in 1935 was 8200. If the population is growing at a rate of 3% per decade, what will it be in 2020? Growth P 1 r t A 82001 0.03 85 10 A 82001.03 A 10,542 8.5 If you have 30 bacteria that double every hour, predict the population after 4 hours. Growth P Amout of Change t where t is how many times it changes. A 302 4 A 3016 A 480 If you have 65 bacteria that triple every hour, predict the population after 4 hours. Growth P Amout of Change t A 653 4 A 6581 A 5265 If you have 120 bacteria that double every 15 minutes, predict the population after 3 hours. Growth P Amout of Change t Note : It is doubling every 15 MINUTES. So, in 3 hours it doubles 4 3 times. A 1202 34 A 1202 12 A 1204096 A 491,520 Suppose the half-life of a certain radioactive material is 20 days and there are 10 grams initially. How much is left after 60 days? Decay P 1 r t A 101 0.5 60 A 100.5 A 100.125 A 1.25 3 20 Suppose the half-life of a certain radioactive material is 15 days and there are 60 grams initially. How much is left after 80 days? Give answer to nearest thousandth. Decay P 1 r t A 601 0.5 80 15 A 600.5 A 1.488 80 15 One Last Thing from Algebra…… Difference of Two Percent Increase / Decrease x100 Original Example: The original population was 100. The new population is 60. What is the percent decrease? Percent 100 60 Decrease x100 100 40% Homework Worksheet