1. Chapter 10.6 Formulas to Memorize: Exponential G & DContinuous Exponential G & D y = final amount a = original amount k = rate or constant t = time

2. Example 1Exponential Decay a)A cup of coffee contains 140 mg of caffeine. If caffeine leaves the body at 10% per hour, how long will it take for half of the caffeine to be eliminated from ones body? 6.5 hours b)A particular car is said to depreciate 15% each year. If the car new was valued at $20,000, what will it be worth after 10 years? $3,937.49

3. Example 2 Example 2Exponential Growth b)A bacteria colony started with 2 bacteria. The colony is growing exponentially at 10% per hour. How long will it take to have 1 million bacteria? a)A town originated in 1910 with 200 people. Since its origination, it has grown exponentially 15% per year. If the population continues to grow at this rate, what will the population be in 2010? 234,862,690 people 137.7 hours

4. Example 3Continuous Exponential Growth b)Jill invested $1000 into a CD account that claims to compound continuously at 10%. How long will it take triple her investment? a)A population of rabbits is growing continuously at 20% each month. If the colony began with 2 rabbits, how many months until they reach 10,000 rabbits? 42.6 months 11.0 years

5. Example 4Continuous Exponential Decay a)The formula for the half life of Carbon-14 is given below. A paleontologist finds the bones of a Wooly Mammoth. She estimates the bones only contain 4% of the Carbon-14 that it would have had alive. Estimate the age of the Mammoth. b)The half life of Sodium-22 is given below. A geologist is studying a meteorite and estimates that it contains only 12% of as much Sodium-22 as it would have when it reached the earths atmosphere. How long ago did the meteorite reach earth. 26,824.0 years old 8.0 years old