Exponential and logarithmic functions

problem
Hyperbolic thinking

Age

16 to 18

Challenge level

Explore the properties of these two fascinating functions using trigonometry as a guide.
problem
A very shiny nose?

Age

16 to 18

Challenge level

This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.
problem
Function pyramids

Age

16 to 18

Challenge level

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?
problem
Prime counter

Age

16 to 18

Challenge level

A short challenge concerning prime numbers.
problem
What's that graph?

Age

14 to 18

Challenge level

Can you work out which processes are represented by the graphs?
problem
Cobalt decay

Age

16 to 18

Challenge level

Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.
problem
Stirling work

Age

16 to 18

Challenge level

See how enormously large quantities can cancel out to give a good approximation to the factorial function.
problem
Back fitter

Age

14 to 18

Challenge level

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
problem
Drug stabiliser

Age

16 to 18

Challenge level

How does the half-life of a drug affect the build up of medication in the body over time?
problem
Extreme dissociation

Age

16 to 18

Challenge level

In this question we push the pH formula to its theoretical limits.