Here is the second post in my ‘FMSP Favourite Problems’ series looking at the problems selected for the Further Maths Support Programme’s favourite problem series of posters.
This second problem I’m not very keen on as it just seems a bit dull.
Unfortunately, the typical GCSE student will not have come across logarithms – though I sort of feel that logarithms should be in the GCSE syllabus – and so couldn’t solve it this way. Unless I have missed something obvious, the only way that they could solve it would be to either calculate the powers of 0.75 until they got the correct value or to plot a graph. Not wanting to plot a graph by hand, I quickly loaded Matlab on my iPad and plotted the following:
In conclusion, as a problem I don’t find this particularly satisfying, however I think it could be used as an opening to an interesting lesson discussing exponential decay, mathematical modelling, ensuring answers you report are meaningful and interpreting graphs.