Understanding Exponential Functions

The video tutorial explains how to write an exponential function from a table. It covers identifying the starting value 'a' and the ratio of change 'b', determining if the function represents growth or decay, and calculating the percent change. The example used involves a table with values showing a decay pattern, where the function decreases by 30% each time.

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

• Determine the function type

• Calculate the percent change

• Find the starting value

• Identify the growth rate

In the context of exponential functions, what does the starting value 'a' represent?

• The final value in the table

• The maximum value in the table

• The value when x equals zero

• The average of all values

If the starting value 'a' is 4, what is the value of f(x) when x equals zero?

• 8

• 6

• 4

• 2

How do you determine the ratio of change 'b' from a table?

• By adding the values

• By dividing the values

• By multiplying the values

• By subtracting the values

What mathematical operation is used to find 'b' from the table values?

• Addition

• Division

• Subtraction

• Multiplication

What is the calculated value of 'b' in the given example?

• 1.2

• 0.5

• 0.7

• 2.0

How can you verify the correctness of the 'b' value?

• By multiplying it across the table values

• By ensuring it is greater than 1

• By checking if it matches the starting value

• By comparing it to the final value

What is the significance of the 'b' value in an exponential function?

• It determines the starting point

• It shows the maximum value

• It indicates the rate of change

• It defines the function's domain

What is the result of multiplying 4 by 0.7 in the context of the table?

• 5.6

• 3.5

• 2.8

• 4.2

Why is it important to verify the 'b' value in an exponential function?

• To ensure the function is linear

• To determine the function's domain

• To confirm the function's accuracy

• To find the function's range