Real Exponents Chapter 11 Section 1

2 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Scientific Notation A number is in scientific notation when it is in the form a x 10 n where 1 < a < 10 and n is a n integer. A number is in scientific notation when it is in the form a x 10 n where 1 < a < 10 and n is a n integer. For any real number b and a positive integer n, the following definitions hold. For any real number b and a positive integer n, the following definitions hold.

3 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Example 1 The volume of the planet Jupiter is x km 3. a.Write this value in standard form x = 1,521,000,000,000,000 b. If the volume of Venus is x km 3, how many times larger is Jupiter than Venus?

4 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Properties of Exponents

5 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Example 2 Evaluate each expression Simplify each expression

6 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Rational Exponents

7 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Example 3 Evaluate each expression Simplify each expression

8 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Rational Exponents Evaluate each expression

9 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Example 5 Simplify Simplify Solve Solve

Exponential Functions Chapter 11 Section 2

11 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Exponential Function You have evaluated functions in which the variable is the base and the exponent is a real number, this is known as a power function. You have evaluated functions in which the variable is the base and the exponent is a real number, this is known as a power function. Functions in the form of y = b x, in which the base b is a positive real number and the exponent is a variable are known as exponential function. Functions in the form of y = b x, in which the base b is a positive real number and the exponent is a variable are known as exponential function.

12 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Graph an Exponential Function a. Consider the graph y = 2 x. x 2x2x2x2xy / /

13 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Characteristics of graphs

14 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Graph an Exponential Function Graph y = 2 x, y = 2 x + 3, and y = 2 x – 2 and compare and contrast.

15 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Graph an Exponential Function Decreasing, continuous, and one-to-one. Same domain and horizontal asymptote. No vertical asymptote or x- intercept. Different y-intercepts

16 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Exponential Functions In general, an equation of the form, y = ab x, where a ≠ 0, b > 0, and b ≠ 1, is called an exponential function with base b. In general, an equation of the form, y = ab x, where a ≠ 0, b > 0, and b ≠ 1, is called an exponential function with base b. There are two types of exponential functions: exponential growth and exponential decay. There are two types of exponential functions: exponential growth and exponential decay. The base of an exponential growth is a number greater than 1. The base of an exponential growth is a number greater than 1. The base of an exponential decay is a number between 0 and 1. The base of an exponential decay is a number between 0 and 1.

17 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Exponential Functions

18 of 19 Pre-Calculus Chapter 11 Sections 1 & 2Example Determine the amount of money in a money market account providing an annual rate of 5% compounded daily if Marcus invested $2000 and left it in the account for 7 years.

19 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Daily Assignment Chapter 11 Sections 1 & 2 Text Book Pg 700 – 701 #21 – 59 Odd Pg 708 – 709 #10 – 14 All; # #19 – 21 All;