UNIT 5 EXPONENTIAL GROWTH AND DECAY CONTINUOUS Exponential

UNIT 5: EXPONENTIAL GROWTH AND DECAY CONTINUOUS Exponential Growth and Decay Percent of change is continuously occurring during the period of time (yearly, monthly, …) Examples: “Continuous Interest”, “Radioactive Half-Life” y = final amount a = original amount k = growth rate constant t = time + = Growth, - = Decay

Example 1 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 c) The population of Raleigh was 212, 000 in 1990 and was 259, 000 in 1998. Write a continuous exponential growth equation, where t is the numbers of years after 1990 for Raleigh’s population.

Example 2 Continuous Exponential Decay #1: The formula for the half life of Carbon-14 The half-life of Carbon-14 is 5760 years which means that every 5760 years half of the mass decays away. a) 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 1 b) A paleontologist finds that the Carbon-14 of a bone is 1/12 of that found in living bone tissue. What is the age of the bone?

#2: 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 #3: Radioactive iodine decays according to the equation where t is in days. Find the half-life of the substance. #4: The half life of Radium-226 is 1800 years. Find the half-life equation for Radium-226. ,