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Applications Growth and Decay Math of Finance

Applications Growth and Decay Math of Finance. Lesson 2.6. Consider Radioactive Half Life. Exponential Growth/Decay. If Y 0 is the initial quantity present The amount present at time t is This is continuous growth/decay Contrast to periodic growth/decay

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Applications Growth and Decay Math of Finance

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  1. ApplicationsGrowth and DecayMath of Finance Lesson 2.6

  2. Consider Radioactive Half Life

  3. Exponential Growth/Decay • If Y0 is the initial quantity present • The amount present at time t is • This is continuous growth/decay • Contrast to periodic growth/decay • Convert between, knowing b = ek • Result is k ≈ r (recall that b = 1 + r)

  4. Exponential Growth/Decay • Given growth data, determine continuous growth function • Initial population = 2500 • Ten years later, population is 4750 • Assuming continuous growth, what is function • Strategy • What is y0? • Use (10,4750), solve for k • Write function

  5. Exponential Growth/Decay • For exponential decay • Recall that 0 < b < 1 and r < 0 • That means k < 0 also • Suppose Superman's nemesis, Kryptonite has half life of 10 hours? • How long until it reaches 30% of its full power and Superman can save the city? • Strategy • Again, find k using .5 and 10 • Then find t using the .3

  6. For continuous compounding Effective Rate • Given • r is stated annual rate • m is number of compounding periods • Then effective rate of interest is • Try it … what is effective rate for 7.5% compounded monthly?

  7. For continuous compounding Present Value • Consider the formula for compounded interest • Suppose we know A and need to know P • This is called the "present value"

  8. Present Value • Try it out … • Find the present value of $45,678.93 if … • Interest is 12.6% • Compounded monthly for 11 months

  9. Assignment • Lesson 2.6A • Page 133 • Exercises 7 – 39 odd

  10. Assignment • Lesson 2.6B • Page 133 • Exercises 16, 18, 20, 22, 41, 43, 45, 47

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