1. 11.2 Exponential Functions
Objectives: Graph exponential functions and inequalities. Solve problems involving exponential growth and decay.

2. 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.

3. 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.

4. 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

5. 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.

6. 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