CONTINUOUS Exponential Growth and Decay

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Presentation transcript:

CONTINUOUS Exponential Growth and Decay UNIT 5 (10.6): 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

Example 1 Continuous Exponential Growth 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? Jill invested $1000 into a CD account that claims to compound continuously at 10%. How long will it take triple her investment?

Example 1 Continuous Exponential Growth c) As of 2000, the populations of China and India can be modeled by C(t) = 1.26e-.009t and I(t) = 1.01e0.015t. According to the models, when will India’s population be more than China’s?

Example 1 Continuous Exponential Growth 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. d) Based on part c), What is the predicted population of Raleigh this year?

Example 2 Continuous Exponential Decay #1: Why is 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 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.

1b) 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.

#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.