Graphical Methods in Exponential Equations

The video tutorial explains how to solve an exponential equation by isolating the exponential part, converting it to a logarithmic equation, and finding the exact solution. It then demonstrates how to calculate a decimal approximation using the change of base formula and verifies the solution through substitution and graphical methods. The tutorial provides step-by-step instructions and highlights key concepts such as the base, exponent, and number in logarithmic equations.

What is the first step in solving an exponential equation?

• Verify the solution graphically

• Isolate the exponential part

• Find the decimal approximation

• Convert it to a logarithmic equation

How can you enter the exponential equation using a keyboard?

• Use the fraction bar and exponent option

• Type the base, use the caret for exponent, and type the quotient

• Directly type the decimal approximation

• Use the logarithm function

What is the base in the logarithmic equation derived from the exponential equation?

• The number 230

• 1.015

• The exponent

• The quotient

What formula is used to convert the logarithmic equation to a decimal approximation?

• Pythagorean theorem

• Change of base formula

• Quadratic formula

• Binomial theorem

What is the approximate value of X rounded to three decimal places?

• 16.500

• 1.015

• 230.000

• 176.962

Which method is NOT used to verify the solution of the equation?

• Graphical method

• Using a calculator

• Using a ruler

• Substitution

What should the product of 16.5 and 1.015 raised to the power of 176.962 approximately equal?

• 176.962

• 16.5

• 1.015

• 230

What is the purpose of adjusting the window in the graphical verification?

• To reset the graph

• To change the color of the graph

• To include the values of X and Y maximums

• To zoom in on the graph

What is the significance of the point of intersection in the graphical method?

• It is irrelevant to the solution

• It indicates an error in calculation

• It verifies the solution of the equation

• It shows the maximum value

What is the final step after verifying the solution graphically?

• Review the video

• Submit the homework

• Adjust the graph settings

• Recalculate the solution