1. 3.1 – Exponential Functions and Their Graphs Ch. 3 – Exponential and Logarithmic Functions

2. Exponential Functions Exponential functions are always in the form: Ex: Graph f(x) = 2 x by hand. ◦ Make a table and graph... ◦ Notable properties: ◦ Horizontal asymptote at y=0 ◦ Domain: All real #s ◦ Range: y > 0 ◦ Always increasing ◦ Y – int: (0, 1) ◦ Note: f(x) = a -x always will be decreasing. (a > 0, a ≠ 1) XY -2.25.5 01 12 24

3. Ex: Graph the function y = -2 x-1 + 1 Parent function is y = 2 x First thing done to the x: -1 (a horizontal shift 1 unit to the right) Next thing done to the x: the negative (flip the whole graph across the x-axis) Last thing done to the x: +1 (vertical shift up 1 unit)

4. The Natural Base e e = 2.718281828… As x  ∞, e occurs in many real-life problems (money, decay, population, etc.)

5. Compound Interest Formula for compound interest: A = balance P = principal r = interest rate n = # times per year interest is compounded t = years When interest is compunded continuously (n  ∞), the formula becomes:

6. Find the graph that matches this function: 1. 2. 3. 4.

7. Sam’s $1000 account is compounded quarterly at a 6% interest rate. How much will he have in that account after 9 years? 1. $1689.48 2. $1787.55 3. $1716.01 4. $1270.24 5. $1709.14

8. Sam’s $1000 account is compounded continuously at a 6% interest rate. How much will he have in that account after 9 years? 1. $1689.48 2. $1787.55 3. $1716.01 4. $1271.25 5. $1722.56