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Unit 4

# 4.3 Rates of Change in Applied Contexts other than Motion

While the title says βOther Than Motion,β 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.

## π Examples

Here are some examples, as an activity, think of the units of the first and second derivatives of these situations.Β
1. A population of rabbits and how many are there each year.
• 1st derivative: rabbits/year
• 2nd derivative: rabbits/year squared.Β
2. Liters of Gas filling a tank and how long it takes in hours.Β
• 1st derivative: liters/hour
• 2nd derivative: liters/hour squared.Β
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.Β
For example, If people are leaving a room, their rate of change would be negative.

## π 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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