Calculating Rates of Change for Nonlinear Graphs

The video tutorial explains nonlinear graphs and how to calculate the rate of change. It covers both average and instantaneous rates of change, using examples like a rocket's takeoff and bacterial cell reproduction. The tutorial provides step-by-step instructions for calculating these rates, emphasizing the importance of understanding changes over time in various contexts, such as science and finance.

What is the key difference between linear and nonlinear graphs?

• Nonlinear graphs have a constant rate of change, while linear graphs do not.

• Linear graphs have a constant rate of change, while nonlinear graphs do not.

• Both linear and nonlinear graphs have a constant rate of change.

• Neither linear nor nonlinear graphs have a constant rate of change.

Why is it important to calculate the average rate of change for a rocket?

• To ensure the rocket does not exceed the speed of light.

• To calculate the distance traveled by the rocket.

• To determine the fuel efficiency of the rocket.

• To ensure the rocket reaches escape velocity.

How do you calculate the average rate of change on a nonlinear graph?

• By measuring the distance between two points on the curve.

• By joining two points with a straight line and finding the gradient.

• By calculating the area under the curve.

• By drawing a tangent at a single point.

In the example of population change, what was the average rate of change per year?

• 150

• 175

• 100

• 200

What is the process to find the instantaneous rate of change at a specific point?

• Draw a straight line between two points.

• Measure the distance from the origin to the point.

• Calculate the area under the curve.

• Draw a tangent at the specific point and find its gradient.