Objectives: I will be able to…  Graph exponential growth/decay functions.  Determine an exponential function based on 2 points  Solve real life problems using exponential functions Vocabulary: exponential function, rule of 72, exponential growth, exponential decay

5.3 Exponential Functions

If given a rate, use Form #1. If not, Form #2 might be more suitable (key words: “double”, “triple”, “half”)

You purchase a baseball card for $54. If it increases each year by 5%, write an exponential growth model. How much will the card be worth in 18 months? 5.3 Exponential Functions You have a new computer for $2100. In 5 years, the computer is worth $500. What is the depreciation rate for the computer?

base b increasing decreasing

 Given 2 points (one must be when x=0 [f(0)=#]) ◦ Plug in the x=0 point  This will eliminate the b term and allow you to solve for a ◦ Plug in the other point and the found value of a  Solve for b ◦ Rewrite the equation with x and y left alone, and a & b replaced with constants

 Plug each point into equation and set up a system of 2 equations:  Try f(2) = 3, f(6) = 2  Math can be messy, it’s ok!

The half-life of a radioactive isotope is 5 days. At what rate does the substance decay each day? Shouldn’t use Form #1 since we have no daily rate- let’s use Form #2!

 Recognizing exponential functions  Remember: ◦ 1) You must have a variable that is an exponent! Linear functions are not exponential ◦ 2) Your base must always be >0 (we do not have negative exponential functions) ◦ 3) To have growth, your base must be >1 ◦ 4) To have decay, your base must be <1 ◦ 5) Domain is always all reals, Range is always >0

Find the exponential equation that contains the following points: (-2, ¼) (1, 2) 1.) 2.) 3.) 4.) Come up with your own growth/decay problem using a real life scenario.

1.) 2.) When a certain medicine enters the blood stream, it gradually dilutes, decreasing exponentially with a half-life of 3 days. The initial amount of the medicine in the blood stream is A 0 millimeters. What will the amount be 30 days later?