Understanding Exponential Functions Concepts

This video tutorial teaches how to identify a third ordered pair in an exponential function using two given pairs. It explains that exponential functions grow by equal factors over equal intervals. Through examples, it demonstrates how to calculate new ordered pairs by adding to the x-coordinate and multiplying the y-coordinate by a consistent factor. The tutorial concludes by applying these concepts to find new ordered pairs in a given exponential function.

What is the main goal of this lesson?

• To learn how to solve linear equations

• To understand how to find a third ordered pair in an exponential function

• To study the properties of logarithms

• To explore quadratic functions

How do exponential functions grow?

• By random fluctuations

• By increasing by a constant amount

• By decreasing over time

• By equal factors over equal intervals

In the example, what is the factor used to multiply the y-values?

• 1/8

• 1/4

• 1/16

• 1/2

What is the new x-value when you add 3 to 5 in the example?

• 9

• 8

• 7

• 6

What is the y-value when x is 8 in the example?

• 3/512

• 3/256

• 3/128

• 3/64

How do you verify the calculated ordered pair in the function?

• By comparing with a table of values

• By graphing the function

• By substituting the x-value back into the function

• By using a calculator

What is the difference between the x-values in the given ordered pairs 3, 4 and 5, 6?

• 4

• 3

• 2

• 1

What operation is used to find the factor needed to multiply the y-values?

• Addition

• Subtraction

• Multiplication

• Division

What is the new ordered pair found in the application example?

• 7, 9

• 6, 8

• 8, 10

• 9, 11

What is the factor used to multiply the y-values from 4 to 6 in the application example?

• 2/3

• 1/3

• 3/2

• 1/2