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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

ApplicationsGrowth and DecayMath of Finance

Lesson 2.6



Exponential growth decay
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)


Exponential growth decay1
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


Exponential growth decay2
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


Effective rate

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?


Present value

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"


Present value1
Present Value

  • Try it out …

  • Find the present value of $45,678.93 if …

    • Interest is 12.6%

    • Compounded monthly for 11 months


Assignment
Assignment

  • Lesson 2.6A

  • Page 133

  • Exercises 7 – 39 odd


Assignment1
Assignment

  • Lesson 2.6B

  • Page 133

  • Exercises 16, 18, 20, 22, 41, 43, 45, 47


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