One Constant, and Everything It Decides

You'll learnto read the growth constant's sign and size correctly, to get a doubling time or a half-life out of it with a logarithm instead of a division, and to keep the constant solution that separating quietly throws away.

Anything whose rate of change is proportional to how much of it there is obeys one equation and has one solution, so the whole topic comes down to reading a single constant correctly. Its sign says grow or decay. Its size sets the doubling time and the half-life, through a logarithm and never through a division. And its units are one over time, which rules out the two readings that cost marks every year. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · THE CONSTANT IS A RATE, NOT AN AMOUNT AND NOT A DURATION · v2

the sign is the direction, and the size is ln 2 divided by it

Before you start

What you're looking at

Quantity against time. The horizontal axis is always time and the vertical axis is the thing being modelled — a population, a mass, a temperature.

The question

Given one constant, what does the model do? Its sign, its size and its units each answer a different exam question, and none of the three answers is a number of years.

Step 1 / 12