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Unit 4

4.3 Rates of Change in Applied Contexts other than Motion

1 min readโ€ขjune 8, 2020


While the title says โ€œOther Than Motion,โ€ really all rates of change are talking about something being in motion. It may not directly say something is in motion but is talking about a change in some way that involved something moving.

๐Ÿ” Examples

Here are some examples, as an activity, think of the units of the first and second derivatives of these situations.ย 

1. A population of rabbits and how many are there each year.

  • 1st derivative: rabbits/year

  • 2nd derivative: rabbits/year squared.ย 

2. Liters of Gas filling a tank and how long it takes in hours.ย 

  • 1st derivative: liters/hour

  • 2nd derivative: liters/hour squared.ย 

You probably get the point!

  • 1st derivative: Measure/time

  • 2nd derivative: Measure/time squared.

Some other situations to apply the rate of change to:

  1. Distance a car travels

  2. People or objects entering or leaving a place

In all these situations, you can use the context to see if the derivative should be positive or negative.ย 

For example, If people are leaving a room, their rate of change would be negative.

๐Ÿ““ Practice

What situations would make the rates of change of the other three situations negative?

  • Rabbits: Population declining (SAD MEME)

  • Liters of Gas: Gas being used and leaving the tank

  • The distance a car travels: Car turns around back to where it came

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