The spread of head lice at a particular school was traced back to a sports trip to a neighbouring school. The spread amongst the students at the school could be modelled by the exponential functionL(t) = 4e^(8t - t^2)k (^ - square) , where t represents the number of weeks after the sports trip, and k is the rate of growth
How many students were initially infected? Justify your answer.
1. Calculate the first derivative. Since you have to use the chainrule one of the factor is (8-2t). This is the only factor which can become zero.
Therefore you'll get t = 4 if you calculate L'(t) = 0.
You have first to define a state called "outbreak is over". Assume the outbreak has passed if only one person is actually infected:When the outbreak was effectively over. Include any assumptions.
I haven't the time yet to do the necessary calculatations in detail but you get
The first value (measured in weeks!) gives the start of the infection and the second value marks the actual end of the infection.