Understanding Linear and Exponential Equations

This video tutorial explains how to write linear and exponential equations to model real-world situations. It covers the use of linear equations for constant changes and exponential equations for percentage changes, providing examples for each. The video also includes additional examples to reinforce the concepts.

What is the initial value of the investment mentioned in the video?

• $8,000

• $9,000

• $9,500

• $10,000

When should you use a linear equation to model a situation?

• When the change is a constant amount per year

• When the change is a constant percent per year

• When the change is random

• When the change is both a constant amount and percent

What is the slope in a linear equation?

• The final value

• The constant rate of change

• The variable

• The initial value

How do you represent a decrease in value by a constant percent per year?

• Using a linear equation

• Using an exponential growth equation

• Using an exponential decay equation

• Using a quadratic equation

What is the base of the exponential decay formula if the decrease is 8%?

• 1.00

• 0.08

• 0.92

• 1.08

In the example of a 14% increase per year, what is the base of the exponential growth formula?

• 0.14

• 1.14

• 0.86

• 1.04

What is the constant rate of change in the linear equation for a decrease of $824 per year?

• 8240

• 824

• 0.824

• -824

Which equation form is used for exponential growth?

• y = mx + b

• y = a(1 + r)^x

• y = a(1 - r)^x

• y = b + mx

What is the decimal representation of a 14% increase?

• 0.14

• 1.14

• 1.04

• 0.86

What is the final equation for a value decreasing by 8% per year?

• v = 9500 - 824t

• v = 9500 * 1.08^t

• v = 9500 + 824t

• v = 9500 * 0.92^t