Exponential and logarithmic functions

$\pH temperature$

problem
pH temperature

Age

16 to 18

Challenge level

At what temperature is the pH of water exactly 7?
problem
Extreme dissociation

Age

16 to 18

Challenge level

In this question we push the pH formula to its theoretical limits.
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
What do functions do for tiny x?

Age

16 to 18

Challenge level

Looking at small values of functions. Motivating the existence of the Maclaurin expansion.
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
Hyperbolic thinking

Age

16 to 18

Challenge level

Explore the properties of these two fascinating functions using trigonometry as a guide.
problem
Blood buffers

Age

16 to 18

Challenge level

Investigate the mathematics behind blood buffers and derive the form of a titration curve.
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
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.