AP® Calculus AB · Unit 7 · Topic 7.1
Modeling Situations with Differential Equations
Watch it explained
- How it worksHow do you translate an English sentence about a rate into a differential equation?
- Worked exampleShow me the differential equation for a colony growing at 3 percent of its size per hour.
- Common mistakeWhy isn't a differential equation solved by integrating both sides as they stand?
- Going furtherWhat changes in the model when growth also depends on how much room is left?
- Ties togetherHow does this general modeling idea turn into the specific exponential growth equation a few topics from now?
Check yourself
Your turn1 of 3
A population P grows at a rate proportional to its size, with proportionality constant k = 0.0618. If P = 619 at some instant, what is dP/dt at that instant?End of topic.