1. Warm-Up 1) A town with a current population of 701,500 has a growth rate of 1.4 percent. Find the multiplier for the rate of exponential growth. 5 minutes 2) The inflation rate of the U.S. is 2.9 percent. What this means is that every year, prices increase by 2.9 percent. If a pound of meat cost $2.55 four years ago, what does it cost now?

2. 6.2.1 Exponential Functions 6.2.1 Exponential Functions Objectives: Classify an exponential function as representing exponential growth or exponential decay

3. Exponential Functions y = x 2 y = 2 x The function f(x) = b x is an exponential function with base b, where b is a positive real number other than 1 and x is any real number. An asymptote is a line that a graph approaches (but does not reach) as its x- or y-values become very large or very small.

4. Exponential Functions Graph y 1 = 2 x and y 2 = When b > 1, the function f(x) = b x represents exponential growth. When 0 < b < 1, the function f(x) = b x represents exponential decay.

5. Example 1 Graph f(x) = 2 x along with each function below. Tell whether each function represents exponential growth or exponential decay. Then give the y-intercept. y = 4(2 x ) exponential growth, since the base, 2, is > 1 y-intercept is 4 because the graph of f(x) = 2 x, which has a y-intercept of 1, is stretched by a factor of 4 exponential decay, since the base, ½, is < 1 y-intercept is 6 because the graph of f(x) = 2 x, which has a y-intercept of 1, is stretched by a factor of 6

6. Practice Graph f(x) = 2 x along with each function below. Tell whether each function represents exponential growth or exponential decay. Then give the y-intercept.

7. Critical Thinking What transformation of f occurs when a < 0 in The graph is reflected across the x-axis.

8. Homework p.367 #11-27 odds

9. Warm-Up Tell whether each function represents exponential growth or decay. 4 minutes 1) f(x) = 12(2.5) x 2) f(x) = 24(0.5) x 3) f(x) = -3(8) x 4) f(x) = 2(4) -x 5) f(x) = 0.75(216) x

10. 6.2.2 Exponential Functions 6.2.2 Exponential Functions Objectives: Calculate the growth of investments under various conditions

11. Compound Interest The total amount of an investment, A, earning compound interest is where P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.

12. Example 1 Find the final amount of a $500 investment after 8 years at 7% interest compounded annually, quarterly, and monthly. compounded annually:= $859.09 compounded quarterly:= $871.11 compounded monthly:= $873.91

13. Practice Find the final amount of a $2200 investment at 9% interest compounded monthly for 3 years.

14. Effective Yield The effective yield is the annually compounded interest rate that yields the final amount of an investment. Suppose you buy a motorcycle for $10,000 and sell it one year later for $13,000. The effective yield would be 30% because you made 30% more ($3,000) than the original price you paid. You can determine the effective yield by fitting an exponential regression equation to two points.

15. Example 2 A collector buys an antique stove for $500 at the beginning of 1990 and sells it for $875 at the beginning of 1998. Find the effective yield. Step 1: Find two points that represent the information after 0 years the stove was worth $500 after 8 years the stove was worth $875 (0,500) (8,875) Step 2: Enter the two points on a list and find the exponential regression equation that fits the points. The multiplier is about 1.0725 1.0725 – 1 = 0.0725= 7.25%

16. Practice Find the effective yield for a painting bought for $100,000 at the end of 1994 and sold for $200,000 at the end of 2004.

17. Homework p.367 #29-35 odds,47,51