ap calc study guides

๐Ÿ‘‘ย  Unit 1: Limits & Continuity

๐Ÿถย  Unit 8: Applications of Integration

โ™พย  Unit 10: Infinite Sequences and Series (BC Only)

4.3 Rates of Change in Applied Contexts other than Motion

#applications

#relatedrates

#change

โฑ๏ธย ย 1 min read

written by


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

continue learning

Slide 1 of 9
Fiveable

Join Our Community

Fiveable Community students are already meeting new friends, starting study groups, and sharing tons of opportunities for other high schoolers. Soon the Fiveable Community will be on a totally new platform where you can share, save, and organize your learning links and lead study groups among other students!๐ŸŽ‰

Fiveable Logo

2550 north lake drive
suite 2
milwaukee, wi 53211

92% of Fiveable students earned a 3 or higher on their 2020 AP Exams.

*apยฎ and advanced placementยฎ are registered trademarks of the college board, which was not involved in the production of, and does not endorse, this product.

ยฉ fiveable 2020 | all rights reserved.