Understanding Linear and Exponential Equations

The video tutorial explains how to identify and differentiate between linear and exponential equations. It describes the forms of these equations and how to determine if they are increasing or decreasing. Exponential equations are characterized by the input variable being in the exponent, with growth or decay determined by the base value. Linear equations follow the slope-intercept form, with behavior determined by the slope. The tutorial provides examples of both types of equations, illustrating their characteristics and behaviors.

What is the main task when given several equations in this problem?

• To solve the equations for x

• To find the roots of the equations

• To graph the equations

• To determine if they are linear or exponential and describe their behavior

Which form does an exponential equation take?

• y = ax^2 + bx + c

• y = a * b^x

• y = a + bx

• y = mx + b

What indicates exponential growth in an equation?

• The coefficient a is zero

• The base b is between 0 and 1

• The base b is greater than 1

• The exponent x is negative

What is the form of a linear equation?

• y = ax^2 + bx + c

• y = mx + b

• y = a + bx

• y = a * b^x

How can you tell if a linear equation is increasing?

• The slope m is positive

• The y-intercept b is negative

• The slope m is zero

• The slope m is negative

In the example of the equation d = 5 * 4^y, what is the behavior of the equation?

• Decreasing because the base is less than 1

• Decreasing because the exponent is negative

• Increasing because the base is greater than 1

• Constant because the base is 1

For the equation h = 170 * 0.9^x, what type of behavior does it exhibit?

• Linear decrease

• Linear increase

• Exponential decay

• Exponential growth

What is the behavior of the linear equation g = -22x + 120?

• Increasing because the slope is positive

• Decreasing because the slope is negative

• Constant because the slope is zero

• Increasing because the y-intercept is positive

In the equation f = 44x - 90, what indicates that the behavior is increasing?

• The y-intercept is negative

• The x-coefficient is zero

• The slope is positive

• The slope is negative

What is the behavior of the equation p = 130 * 1.1^t?

• Exponential decay

• Linear decrease

• Exponential growth

• Linear increase