11.2 Exponential Functions Objectives: Graph exponential functions and inequalities. Solve problems involving exponential growth and decay.

A function in the form y=b^x, where x is a real number. Power Function: A function in the form y=b^x, where x is a real number. Ex. 1) Graph y=3^x by hand. Then graph it on a calculator. Characteristics of graphs of y=b^x on pg. 705 Ex. 2) a.) Graph the exponential functions y=2^x, y=2^x + 3, and y=2^x – 2 on the same set of axes. Compare and contrast the graphs. b.) Graph y=(⅓)^x, y=5(⅓)^x , and y=-1(⅓)^x Compare and contrast.

Ex. 3) A car depreciates or loses value at the rate of 20% per year. If the car originally cost $20,000, the depreciation can be modeled by the equation y=20,000(0.8)^t; where y is the depreciation and t is the time in years. Find the value of the car at the end of 2 years. Graph it.

Exponential Decay: occurs when a quantity decreases exponentially over time. occurs when a quantity increases exponentially over time. Exponential Growth: N = No (1 + r)^t N→final amount No→initial amount r→rate as a decimal t→# of time periods

Ex. 4) The average growth rate of the population of a city is 7.5% per year and is represented by the formula y=A(1.075)^x where x is the number of years and y is the most recent population of the city. The city’s population “A” is now 22,750 people. What is the expected population in 10 years? Compound Interest: A=P(1 + r/n)^nt A→final amount P→principal r→annual interest rate t→# of years n →# of times interest is paid or compounded each year.

Ex. 5) How much should Sabrina invest now in a money market account if she wishes to have $9,000 in the account at the end of 10 years? The account provides an APR of 6% compounded quarterly. Ex. 6) Graph y>3^x + 1