Writing Exponential Equations from Graphs: Two-Point Method

This lesson teaches how to write exponential equations by analyzing graphs. It covers identifying exponential growth and decay, understanding the general equation y = aB^X, and addresses common misconceptions. Two scenarios are explored: one with a known Y-intercept and another with an unknown Y-intercept, demonstrating how to derive equations using data points from graphs.

What does a graph represent if it shows an increase from left to right?

• Exponential growth

• Quadratic growth

• Exponential decay

• Linear growth

In an exponential equation, what does the constant multiplier 'B' indicate when it is greater than one?

• Exponential decay

• Linear relationship

• Exponential growth

• Quadratic relationship

If the Y-intercept is known, what is the initial value 'A' in the equation y = a * b^x?

• The value of Y when X is 0

• The value of X when Y is 0

• The value of Y when X is 1

• The constant multiplier

When the Y-intercept is unknown, how many data points are needed to determine the explicit equation?

• Four

• Three

• One

• Two

What is the first step in finding the explicit equation when the Y-intercept is unknown?

• Determine the constant multiplier

• Graph the data points

• Obtain two known data points

• Solve for the initial value

In the example where B is found to be 4, what is the value of A?

• 0

• 1

• 4

• 2

What is the final step in writing the exponential equation when the Y-intercept is unknown?

• Verify the data points

• Substitute the values of A and B into the general equation

• Graph the equation

• Find the Y-intercept