1. a = c b Exponent Base Solution Rational Exponents Irrational Exponents
We have worked with ______________ _______________ in the past, but in this section will begin to look at __________________ ____________________.
In order to put irrational exponents into the calculator, use the ______________ key.
Rational Exponents
Irrational Exponents
Caret

2. 0.117 0.113 5.900 0.465 3640.950 Examples: 2-3.1 = _____________
2-∏ = _____________
125/7 = ___________
(0.6) 3/2 = _____________
e 8.2 = _____________
0.117
0.113
5.900
0.465

3. What is e?
Much like π, e is a special irrational number used in math
It occurs in natural exponential growth and decay situations
It was discovered by a mathematician Leonard Euler
Called the natural base e or Euler’s number

5. Exponential functions 𝒚= 𝒂 𝒙
Exponential expressions can also be written as ___________________ ________________, which take the form _______________________.
Let’s look at the graphs formed by a standard exponential function:
Exponential functions
𝒚= 𝒂 𝒙
𝟎<𝒂<𝟏
𝒂>𝟏

6. reflection translation Form of the Function Changes to the Graph
When the graph of the exponential function 𝑦= 𝑎 𝑥 is modified, the rules of ______________ and ___________________ should be applied.
reflection
translation
Form of the Function
Changes to the Graph
y = a (x-c)
y = a (x+c)
y = a x - c
y = a x + c
y = - a x
y = a - x
move right c units
move left c units
move down c units
move up c units
Reflected in x axis
Reflected in y axis

7. Exponential functions can also be applied to ideas of compound interest using the
formulas __________________________ for compounding periodically and
__________________________ for compounding continuously.
𝑨=𝑷 (𝟏+ 𝒓 𝒏 ) 𝒏𝒕
𝑨=𝑷 𝒆 𝒓𝒕

8. Can you identify? Domain: Range: Y- intercept: Increase/decrease:
Exponential Function Examples:
Use your calculator to help you draw the function 𝑦 = 𝑒 𝑥 .
Apply rules of transformations to draw 𝑦 = − 𝑒 𝑥−2 + 4 on the same graph, showing the reflections and translations in the graph.
Can you identify?
Domain:
Range:
Y- intercept:
Increase/decrease:
Asymptotes:

9. 2. A total of $12,000 is invested at an annual interest rate of 9%
2. A total of $12,000 is invested at an annual interest rate of 9%. Find the balance after five years if it is compounded.
Quarterly (n = 4).
Monthly (n = 12)
Continuously (𝐴 = 𝑃 𝑒 𝑟𝑡 ).