Analyzing Rates and Functions

This lesson explores increasing and decreasing functions through real-world examples. It covers nonlinear functions, constant and variable rates of change, and includes exercises on running rates, dog growth, battery charging, and Ferris wheel motion. The lesson emphasizes understanding the graphical representation of these concepts.

What type of function is needed to describe relationships that cannot be modeled by linear functions?

• Quadratic function

• Exponential function

• Nonlinear function

• Linear function

How far does Aleph run in the first 15 minutes?

• 4 miles

• 3 miles

• 2 miles

• 1 mile

What is Aleph's running rate throughout his run?

• 4 miles every 25 minutes

• 3 miles every 20 minutes

• 2 miles every 15 minutes

• 1 mile every 10 minutes

How far does Shannon run between 0 to 15 minutes?

• 1 mile

• 1.5 miles

• 2.5 miles

• 2 miles

What happens to Shannon's running rate as she continues on the trail?

• It fluctuates

• It decreases

• It increases

• It remains constant

What characterizes a linear function in terms of rate of change?

• Increasing rate of change

• Decreasing rate of change

• Constant rate of change

• Variable rate of change

What type of growth does a large breed dog experience from birth to six months?

• Slow growth

• Rapid growth

• Constant growth

• No growth

How does the battery charge of Nikka's laptop change over time?

• It increases at a constant rate

• It fluctuates

• It remains constant

• It decreases

What is the diameter of the ferris wheel based on the graph?

• 30 feet

• 35 feet

• 40 feet

• 45 feet

How many revolutions does the ferris wheel complete in 40 seconds?

• 4 revolutions

• 3 revolutions

• 5 revolutions

• 6 revolutions