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Understanding Exponential Growth and Decay: Radium and Investment Calculations

In this lesson, we explore exponential growth and decay functions through two practical problems. First, we examine a case study involving radium, which has a half-life of 1620 years. We calculate the remaining amount after 10,000 years given an initial amount of 1.5 grams present after 1000 years. Next, we analyze a financial scenario where a $10,000 investment doubles in 5 years. We will determine the initial interest rate and calculate the future value after 12 years with continuous compounding.

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Understanding Exponential Growth and Decay: Radium and Investment Calculations

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  1. AP Calculus AB Day 4 Section 6.2 Perkins

  2. Exponential Growth and Decay Function rate of growth or decay final amount initial amount Half-life Doubling-time

  3. 1. Radium has a half-life of 1620 years. If 1.5 grams is present after 1000 years and Radium follows the law of exponential growth and decay, how much is left after 10,000 years?

  4. 2. An initial investment of $10,000 takes 5 years to double. If interest is compounded continuously… a. What is the initial interest rate? b. How much will be present after 12 years?

  5. AP Calculus AB Day 4 Section 6.2 Perkins

  6. Exponential Growth and Decay Function Half-life Doubling-time

  7. 1. Radium has a half-life of 1620 years. If 1.5 grams is present after 1000 years and Radium follows the law of exponential growth and decay, how much is left after 10,000 years?

  8. 2. An initial investment of $10,000 takes 5 years to double. If interest is compounded continuously… a. What is the initial interest rate? b. How much will be present after 12 years?

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