In (a)–(e), say whether the quantity is changing in a linear or exponential fashion.
- A savings account, which earns no interest, receives a deposit of $723 per month.
- The value of a machine depreciates by 17% per year.
- Every week, \(9/10\) of a radioactive substance remains from the beginning of the week.
- A liter of water evaporates from a swimming pool every day.
- Every 124 minutes, \(1/2\) of a drug dosage remains in the body.
Commentary
This task gives a variet of real-life contexts which could be modeled by a linear or exponential function. The key distinguishing feature between the two is whether the change by equal factors over equal intervals (exponential functions), or by a constant increase per unit interval (linear functions). The task could either be used as an assessment problem on this distinction, or used as an introduction to the differences between these very important classes of functions.