Exponential and logarithmic functions

There are 30 NRICH Mathematical resources connected to Exponential and logarithmic functions
Gosh Cosh
problem

Gosh Cosh

Age
16 to 18
Challenge level
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Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.
Hyperbolic thinking
problem

Hyperbolic thinking

Age
16 to 18
Challenge level
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Explore the properties of these two fascinating functions using trigonometry as a guide.
A Very Shiny Nose?
problem

A Very Shiny Nose?

Age
16 to 18
Challenge level
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This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.
Function Pyramids
problem

Function Pyramids

Age
16 to 18
Challenge level
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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?
Prime counter
problem

Prime counter

Age
16 to 18
Challenge level
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A short challenge concerning prime numbers.
What's that graph?
problem

What's that graph?

Age
14 to 18
Challenge level
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Can you work out which processes are represented by the graphs?
Cobalt decay
problem

Cobalt decay

Age
16 to 18
Challenge level
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Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.
Stirling work
problem

Stirling work

Age
16 to 18
Challenge level
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See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Back fitter
problem

Back fitter

Age
14 to 18
Challenge level
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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?

Drug stabiliser
problem

Drug stabiliser

Age
16 to 18
Challenge level
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How does the half-life of a drug affect the build up of medication in the body over time?