Exponential Functions and Sequences

This video tutorial explains how to write exponential equations of the form y = ab^x using a table of values. It covers identifying the initial value 'a' when x is zero and determining the growth or decay factor 'b' by analyzing the multiplier between consecutive values. The tutorial provides examples and practice problems to reinforce the concepts, guiding viewers through the process of formulating the exponential equation and verifying their solutions.

What is the general form of an exponential equation?

• y = ax^b

• y = ab^x

• y = a/b^x

• y = a + bx

In the equation y = ab^x, what does 'a' represent?

• The exponent

• The initial value

• The decay factor

• The growth factor

How do you find the initial value 'a' in an exponential equation?

• By finding the value of y when x is zero

• By finding the value of x when y is zero

• By multiplying y by x

• By dividing y by x

What is the role of 'b' in the equation y = ab^x?

• It is the exponent

• It is the growth or decay factor

• It is the initial value

• It is the constant

If y = 3 * 2^x, what is the growth factor?

• x

• 2

• 6

• 3

How can you quickly determine the multiplier 'b'?

• By adding the current value to the previous value

• By subtracting the previous value from the current value

• By dividing the current value by the previous value

• By multiplying the current value by the previous value

What operation undoes multiplication when finding 'b'?

• Division

• Subtraction

• Exponentiation

• Addition

What is the equation for y if a = 3 and b = 2?

• y = 3^x * 2

• y = 3 + 2^x

• y = 3 * x^2

• y = 3 * 2^x

In function notation, how is y = 3 * 2^x written?

• f(x) = 3 * 2^x

• f(x) = 3 + 2^x

• f(x) = 3 * x^2

• f(x) = 3^x * 2

What is the initial value 'a' if x = 0 and y = 1/4?

• 1/4

• 1/2

• 1

• 2