Exponential and logarithmic functions

There are 30 NRICH Mathematical resources connected to Exponential and logarithmic functions
What's that graph?
problem
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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?

Mixing \pH
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Mixing ph

Age
16 to 18
Challenge level
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Use the logarithm to work out these pH values
Exponential Trend
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Exponential trend

Age
16 to 18
Challenge level
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Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.
Back fitter
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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?

Integral Equation
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Integral equation

Age
16 to 18
Challenge level
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Solve this integral equation.
Dating made Easier
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Dating made easier

Age
14 to 16
Challenge level
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If a sum invested gains 10% each year how long before it has doubled its value?
Equation Attack
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Equation attack

Age
16 to 18
Challenge level
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The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.
Log Attack
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Log attack

Age
16 to 18
Challenge level
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Solve these equations.
The Legacy
problem
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The legacy

Age
14 to 16
Challenge level
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Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?
Harmonically
problem
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Harmonically

Age
16 to 18
Challenge level
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Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?