Applications Growth and Decay Math of Finance Lesson 2.6

Consider Radioactive Half Life 2

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 Convert between, knowing b = e k Result is k ≈ r (recall that b = 1 + r) 3

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 y 0 ? Use (10,4750), solve for k Write function 4

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 5

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? 6 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" 7 For continuous compounding

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

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

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