SFM Productions Presents: Another saga in your continuing Pre-Calculus experience! 3.1Exponential Functions and their Graphs

p224#7-27, 33-43, Do EOO unless you get something wrong. Then do the others. I will probably start doing tri-weekly 1 question pop quizzes to ensure your compliance. Homework for section 3.1 You will need to know all the properties of exponents listed on the bottom of page A14. Otherwise, you might as well hang it up …

So far, we have dealt with algebraic functions. Now, we will work with: transcendental functions: Exponential Logarithmic An exponential function with base “a”: is denoted by:

Let’s graph some … f(x) = a x x2x2x -2 x 2 -x -2- x ¼½124¼½124 - ¼ - ½ ½¼421½¼ -2 - ½ - ¼ HA: y = 0

Some more examples f(x) = 1 x f(x) = 1.5 x f(x) = 2 x f(x) = 4 x f(x) = 20 x HA: y = 0

Domain: For all: f(x) = a x (where a is positive) Range: Intercept: HA: Increasing: Decreasing

f(x) = e x f(x) = … x e is called the natural base

Shifting f(x) = 2 x f(x) = 2 x + 3 f(x) = 2 x - 4 What is new asymptote???

Shifting f(x) = 2 (x+3) f(x) = 2 x What is new asymptote??? f(x) = 2 (x-4) What is new asymptote???

Making money … You have “P” amount of money … and you wisely want to invest that money … P stands for Principal …… N stands for Compounding: each time you calculate interest. R stands for Interest Rate …… T stands for Time … (usually in years)

How to calculate your new balance … (A) P: your original chunk of change. r: is to be expressed as a decimal. n: is the number of compoundings per year. t: is the number of years you leave your money cooking in the bank.

How to calculate your new balance if your compounding is done continuously … (the best thing to look for) Example You have $12,000 you want to invest at a rate of 9% for a time of 5 years. How much money will you have if compounding is done: a) Quarterly b) Monthly c) continuously

You have $12,000 you want to invest at a rate of 9% for a time of 5 years. How much money will you have if compounding is done: a) Quarterly b) Monthly c) Continuously

Radioactive Decay The amount of Plutonium remaining at Chernobyl (Soviet Union, 1986) is modeled by: Assuming there were initially 10 pounds of plutonium present, how much is left now? (2011) How much will be left in 100,000 years?

Go! Do!