Exponential and logarithmic functions

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?

If a sum invested gains 10% each year how long before it has doubled its value?

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?

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

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.

Solve this integral equation.

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.

Solve these equations.

Can you locate these values on this interactive logarithmic scale?

Use the logarithm to work out these pH values