1.2 Linear Approximate Rate - notes

# 1.2 Linear Approximate Rate - notes - Objective[1.2 Notes...

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Objective [1.2] – Notes Understand that the average rate of change of a relationship is a linear estimate of its actual rate of change. There is just one basic idea to learn in this objective but it’s VERY important. It’s not too hard to understand if we go back to the driving position/speed/acceleration example in the previous objective 1.1. In the previous objective you hopefully were reminded that a relationship that is linear has a constant rate and thus now know that all non-linear relationships (ones that don’t graph as a straight line on a Cartesian plot) have rates that change at every input. This always changing rate of non-linear relationships is unfortunate when we want to let someone know how fast some relationship is growing. We just c an’t “pin it down” . It is always changing. Think for a moment. If someone wanted know “how fast” they were going on a trip they wouldn’t record their speed at every second and then graph the data. They wouldn’t take all that data and average all those speeds to get an average speed. No instead they might write down the initial miles on the odometer noting the time and then the ending miles on the odometer and the final time. From this they could compute how many miles were driven and how many hours it took. From the last objective we know that rate is output/input so dividing the miles driven by the time one gets an “overall” average rate. In other words if they could have driven that average speed constantly for the entire trip they

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1.2 Linear Approximate Rate - notes - Objective[1.2 Notes...

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