1. 5.2 Exponential Functions and Graphs

2. Graphing Calculator Exploration Graph in your calculator and sketch in your notebook: a) b) c) d)

3. Exponential Growth: b>1 b≠1, b>0 Increasing Asymptote: y=0 Domain: (-∞,∞) Range: (0,+∞)

4. Exponential Decay: 0<b<1 b≠1, b>0 Decreasing Asymptote: y=0 Domain: (-∞,∞) Range: (0,∞)

5. Exponential Functions What happens when a < 0? Given the function: The graphs are reflected about the x-axis

6. Graphing Calculator Exploration Graph in your calculator, sketch in your notebook and make a table of the ordered pairs for -2 ≤ x ≤ 2. e) f) g)

7. Exponential Functions When a>1, the graph of y = b x vertically stretches When 0>a>1, the graph of y = b x vertically shrinks Given the function: How does the value of a affect the graph of y = b x ? “multiply y’s by a”

8. y = ab x–h + k How do h and k affect the graph of y = ab x ? h causes y = ab x to shift horizontally h units  right if h > 0 or left if h < 0 k causes y = ab x to shift vertically k units  up if k > 0 or down if k < 0

9. Practice Graph. Use integer values of x from -2 to 2 in your table. Describe how the graph can be obtained from the graph of the basic exponential function.

10. Compound Interest A = the amount of money that you have after a certain number of years P = the principal (initial quantity of money) r = percentage rate (change to a decimal) t = time in years n = number of times compounded per year

11. Practice 5) You deposit $5000 into an account, which earns 6% compound interest. Assuming that you do not withdraw any money from the account, after 4 years, how much money will you have… a) if the account is compounded monthly? b) if the account is compounded quarterly? c) if the account is compounded daily?

12. Let’s say that: r=100% P=1 t=1 Compound Interest That yields: What happens to A as n  ∞ ?

13. Natural base, e - the Euler # Use the e button on your calculator to find e 1.35 to four decimal places. Graph: y = e x Graph: y = e − x e ≈ 2.718281828