Mistake Master
Mistake Master · AP Calculus · Unit 7 · Step-Through Animation
A Sentence About a Rate
You'll learnto turn a description in English into an equation with a derivative on one side, to attach the constant to the whole phrase that follows "proportional to", and to read a finished model's behavior without solving it.
A differential equation is a sentence about a rate, written in symbols. Nothing in this topic gets solved, and nothing needs to be: the model is the deliverable. Two moves carry the whole thing — words like grows and rate of change put a derivative on the left, and whatever phrase follows "proportional to" is exactly what the constant multiplies, in full. Twelve short steps; press Next for each one.
A rate goes on the left, and k multiplies the whole phrase
Before you start
What you're looking at
A ledger. The English phrase sits on the left, an arrow points right, and the equation it produces sits on the right; violet is a rival reading.
The question
Which side of the equation is the rate, and what exactly does the constant multiply? Nothing here gets solved.