Exponential Function Context and Data Modeling

So far the models were handed to you: $N(t) = 256(1.5)^{t}$, $C(t) = 160(0.87)^{t}$. Real problems don't start with a formula. They start with a sentence (“the app grows 6% a week”, “caffeine has a half-life of about 5 hours”) or with a few measurements. This note is about turning that information into a model, and then reading the model back in the language of the situation.