Exponential and logarithmic functions

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Exponential Trend

Age

16 to 18

Challenge level

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.
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Integral Equation

Age

16 to 18

Challenge level

Solve this integral equation.
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Log Attack

Age

16 to 18

Challenge level

Solve these equations.
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Harmonically

Age

16 to 18

Challenge level

Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?
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The Legacy

Age

14 to 16

Challenge level

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?
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Dating Made Easier

Age

14 to 16

Challenge level

If a sum invested gains 10% each year how long before it has doubled its value?
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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?
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What's That Graph?

Age

14 to 18

Challenge level

Can you work out which processes are represented by the graphs?
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Equation Attack

Age

16 to 18

Challenge level

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.
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Power Match

Age

16 to 18

Challenge level

Can you locate these values on this interactive logarithmic scale?