Chapter 10 6 Formulas to Memorize Exponential G

Chapter 10. 6 Formulas to Memorize: Exponential G & D Continuous Exponential G & D y = final amount a = original amount k = rate or constant t = time

Example 1 Exponential 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

Example 2 Exponential Growth 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 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? 137. 7 hours

Example 3 Continuous Exponential Growth 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 b) Jill invested $1000 into a CD account that claims to compound continuously at 10%. How long will it take triple her investment? 11. 0 years

Example 4 Continuous 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. 26, 824. 0 years old 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. 8. 0 years old