Chapter 8 Section 2 Properties of Exp. Functions

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Chapter 8 Section 2 Properties of Exp. Functions Algebra 2 Notes April 30, 2009

Warm-Ups 1) The birth rate of a colony of ants is 60% per year. The Death rate is 46%. Assume the starting population is 650 ants. A) What is the difference between the birth and the death rates? B) Is the population increasing or decreasing? C) Write an equation that could model this situation. D) Using this equation: how big will the colony be after 4 years? 2) Challenge: Write a story problem that could be modeled with the equation y=20(1.1)^x

Half Life (Page 440) The half-life of a radio active substance is the time it takes for half of the material to decay. A hospital prepares a 100-mg supply of technetium-99m, which has a half life of 6 hours. How much technetium-99m is left after 6 hours? After 12 hours? 18 hours? Write an exponential function to find the amount of technetium-99m after x number of hours Use your equation to find the amount of material left after 75 hours.

Asymptotes Graph the equation from the last example in your calculator Use the window -30<x<100, count by 10; -100<y<400, count by 40 What value does the graph seem to be approaching but never cross? This is called an asymptote (pronounced: ass-im-tote… excuse the foul language!) In particular this is a horizontal asymptote

And Again…. Study this equation: Use your previous knowledge about ‘a’, ‘h’ and ‘k’ to make a conjecture about what they mean in terms of the graph of this type equation (write them down real quick!)

Translations You were right!!!!  ‘a’ will stretch or shrink the graph ‘h’ will translate the graph horizontally (x-axis) (+ moves left, - moves right!) ‘k’ will translate the graph vertically (y-axis) In other words, ‘k’ moves the asymptote from 0 to k

Introducing….. The number …… e!!! e represents the number 2.71828128… e is used to represent continual growth or decay (think ‘e’ for exponential growth and decay) e is a number like pi It is an irrational number (it cannot be written as a fraction)

Continuously Compounded Interest Formula: Amount in Account Rate of annual interest Time in years Principal (starting) Amount

Example Suppose you invest $1050 at an annual interest rate of 5.5% compounded continuously. How much money, to the nearest dollar, will you have in the account after 5 years? P = r = A = what you’re solving for t =

You Try Suppose you invest $1300 at an annual interest rate of 4.3% compounded continuously. Find the amount you will have in the account after 3 years. How much profit did you make in 3 years??

Homework #57 Page 442 #15-17, 19, 21, 23, 24-26, 30, 32-36, 40, 41.