Unit 12
Exponents and logarithms.
Amounts that grow by multiplying: exponential growth, rates in per cent, logarithms that ask "how many times?", and half-life.
Before this unit
The unit, lesson by lesson
Lessons
4 lessons · 21 practice questions · about an hour
Growth by multiplying
An amount multiplied by the same number at every step: why ten doublings give more than a thousand, how to write it as a power, and why such growth always overtakes a steady addition in the end.
Growth rates
Growth by so many per cent at every step is multiplying by a fixed factor: how to turn a percentage into a factor, why ten steps of ten per cent are more than a hundred per cent, how long it takes to double, and what happens when an amount shrinks by a percentage.
Logarithms
A logarithm answers the question "how many times do you multiply?": logarithms to base two and base ten, the log scale on which exponential growth is a straight line, and why the logarithm of a product is a sum.
Decay and half-life
Radioactive decay is exponential decay: in every half-life, half of what was there is left. How much is left after several half-lives, how long it takes to reach a given fraction, and why a small sample does not give exact numbers.