Exponential Functions and Geometric Sequences

This video tutorial introduces module three, focusing on geometric sequences and exponential functions. It explains how to identify constant ratios in sequences using multiplication and division. The tutorial provides examples and calculations to reinforce understanding. It then introduces exponential functions, explaining their properties and how to translate geometric sequences into exponential functions. The video also covers rewriting exponential functions using exponent rules and demonstrates practical applications by writing exponential functions from tables.

What is the first step in identifying the constant ratio in a geometric sequence?

• Multiply the x-values

• Divide the second y-value by the first

• Subtract the y-values

• Add the y-values

If you multiply -2 by 3, what is the result?

• -3

• 6

• 3

• -6

What does the constant ratio represent in a geometric sequence?

• The difference between y-values

• The sum of the y-values

• The number you multiply each y-value by to get the next

• The sum of the x-values

What is the general form of an exponential function?

• a + bx

• a - bx

• a * b^x

• a / b^x

In the exponential function a * b^x, what does 'a' represent?

• The exponent

• The constant ratio

• The variable

• The initial amount

How do you type the exponent in an exponential function using a keyboard?

• Shift + 8

• Shift + 6

• Ctrl + 6

• Ctrl + 8

What is the equivalent of 2 raised to the negative 1 power?

• Both 1/2 and 0.5

• 2

• 1/2

• 0.5

In the function f(x) = -2/3 * 3^x, what is the constant ratio?

• -2

• x

• 3

• -2/3

What is the first step in writing an exponential function from a table?

• Adjust the parameters

• Copy the table

• Move the sliders

• Add the sliders

In the function f(x) = 4 * (1/2)^x, what is the value of 'b'?

• 4

• 2

• x

• 1/2