Writing Exponential Functions from Tables

The video tutorial explains how to write exponential functions from tables. It covers the form of exponential functions, identifying the y-intercept (A value) and the common ratio (B value), and provides step-by-step instructions. Several examples demonstrate how to calculate A and B values using consecutive points from tables, ensuring the calculations are reasonable. The tutorial emphasizes checking the multiplication of values to verify the correctness of the derived function.

What is the general form of an exponential function?

• y = a - b^x

• y = a * b^x

• y = a + b^x

• y = a / b^x

What does 'a' represent in the exponential function formula?

• Y-intercept of the function

• Variable of the function

• Slope of the function

• Base of the exponent

How do you find the 'b' value when given a table of values?

• Subtract y2 from y1

• Divide y2 by y1

• Add y2 to y1

• Multiply y2 by y1

What does it mean for coordinates to be consecutive in a table?

• They are in a random order

• They follow one after another

• They are evenly spaced

• They are all even numbers

In the example, if the y-intercept is 18 and the next y value is 6, what is the 'b' value?

• 1/2

• 2

• 1/3

• 3

What should you check after calculating 'a' and 'b' values?

• Their product

• Their sum

• Their reasonableness

• Their divisibility

If 'a' is 5 and the function multiplies by 5 each step, what is the function's formula?

• y = 5 + 5^x

• y = 5 / 5^x

• y = 5 - 5^x

• y = 5 * 5^x

What does a 'b' value of 2/3 indicate about the function's behavior?

• It decreases slowly

• It decreases rapidly

• It increases rapidly

• It increases slowly

If the initial y value is 530 and the next is 636, what is the 'b' value?

• 1.1

• 1.4

• 1.2

• 1.3

What is the exponential function formula if 'a' is 0.25 and 'b' is 4?

• y = 0.25 / 4^x

• y = 0.25 * 4^x

• y = 0.25 - 4^x

• y = 0.25 + 4^x