1. 4.1 Exponential Growth Functions Retesting Opportunity: Dec. 1 4.1-4.2 Quiz: Dec. 3 Performance Exam: Dec. 4

2. Vocabulary  An exponential function has the form y = ab x, where a = 0 and the base b is a positive number other than 1.  If b > 1, then the function y = ab x is an exponential growth function, and b is called the growth factor.  An asymptote is a line that a graph approaches more and more closely…but NEVER touches!

3. Graph of y = 2 x The graph y = 2 x approaches the x-axis but never reaches it…we call the x-axis an asymptote

4. Example 1:  Graph y = 5 x

5. Example 2:  Graph y = (-1/4)2 x

6. Example 3:  Graph y = 3 2 x+1 + 2 Let’s look at y = 32 x first

7. Vocabulary  Exponential Growth Model When a real-life quantity increases by a fixed percent each year (or other time period), the amount y of the quantity after t years can be modeled by the equation y = a(1 + r) t, where a is the initial amount and r is the percent increase expressed as a decimal. Note that quantity 1 + r is the growth factor.

8. Example 4:  The population of the United States was 248,718,301 in 1990 and was projected to grow at a rate of about 8% per decade. Predict the population, to the nearest hundred thousand, for the year 2010.

9. Solution:  To obtain the growth factor for exponential growth, add the growth rate to 100%.  What is our growth factor??  Write the expression for the population t decades after 1990. 248,718,301 · (1.08) t 108% or 1.08

10. Solution continued:  How many decades is it from 1990 to 2010? 2 decades  We substitute 2 in for t and solve… The predicted population for 2010 is 290, 100, 000

11. Compound Interest Formula  The total amount of an investment, A, earning compound interest is:  where P is the principle (starting amount), r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years.

12. Example 5:  You deposit $3000 in an account that pays 6% interest compounded annually. In about how many years will the balance double?

13. Homework:  P. 132 #1-15odd