Learning Resources

Lesson

The following hints and suggestions are offered to help you progress through these case studies and successfully complete each.

• Case Study 1: Charity Fundraiser
• Case Study 2: Population Change
• Extension: Rate of Change

Case Study 1: Charity Fundraiser

• The function can be found by using quadratic regression and/or a system of equations.
• Using graphing technology, graph the function and interpret the rates of change from the graph as required.
• Profit is found by multiplying the number of rolls sold by the profit per roll. Of course, for each roll the profit is the difference between the selling price and the cost.
• Read instantaneous rates of change from the graph and/or calculate by using the slope formula for secants very close to the point to determine the slope of the tangent line.

Case Study 2: Population Change

• Read from the table where the population is increasing (+) no change (0), and decreasing (-).
• Create linear functions using two points in the point slope form of the equation and describe what a linear rate of change means.
• Find the quadratic equation by using regression analysis and/or a system of equations.
• Read instantaneous rates of change from the graph and/or calculate by using the slope formula for secants very close to the point to determine the slope of the tangent line.

Extension: Rate of Change

Refer to question 29, section 2.2 , page 94 for the setup for this extension. Obtain a copy of its solution found in the Teacher Resource Book from your in school teacher.

The formula for the volume of a sphere is . In fact the change in volume as a function of the change in radius is , the surface area of the sphere.

Activity

Depending on the time you have, complete at least one of the Case Studies or the Extension on pages 97 - 99 in your text. If you have the time and interest complete any two or all three of them.

Test Yourself

Discuss issues surrounding these case studies/extension with your teacher and on/or classmates.