Exponential Functions and Graphs

The video tutorial explains how to find an exponential function for a semi-log graph. It begins by identifying the graph's characteristics, such as the linear x-axis and logarithmic y-axis. The tutorial then calculates the slope of the line and converts the logarithmic equation into an exponential form. Finally, it rewrites the equation in the standard exponential form and provides decimal approximations for the constants involved.

What type of graph is used when the x-axis is linear and the y-axis is logarithmic?

• Semi-log graph

• Exponential graph

• Log-log graph

• Linear graph

What is the y-intercept of the line on the semi-log graph?

• -1

• 1

• 0

• 2

How do you calculate the slope of the line on the graph?

• Change in x divided by change in y

• Difference between x and y changes

• Change in y divided by change in x

• Sum of x and y changes

What is the slope of the line on the semi-log graph?

• 1/3

• 3/2

• 2/3

• 1/2

In the equation Y = MX + B, what does M represent?

• Exponent

• X-intercept

• Slope

• Y-intercept

What is the base of the natural logarithm used in the conversion?

• π

• e

• 2

• 10

How is the exponential equation rewritten using the product property of exponents?

• G(x) = E^(2/3x) * E^(-1)

• G(x) = E^(x) * E^(2/3)

• G(x) = E^(x) / E^(2/3)

• G(x) = E^(2/3) + E^(-1)

What is the decimal approximation of 1/E to four decimal places?

• 0.6931

• 0.3679

• 0.5000

• 1.0000

What is the decimal approximation of E^(2/3)?

• 1.9477

• 2.7183

• 1.0000

• 0.5000

What does the final exponential function represent?

• A linear graph

• A log-log graph

• A semi-log graph

• A quadratic graph