9709 P31 - Jun 2024 - Q11 - 11 marks
9983
A field has 300 plants. At time t, x are infected; dx/dt is proportional to the product of infected and uninfected numbers. Treat x,t as continuous. Initially x=1 and dx/dt=0.2.
(a) Show \(dx/dt=x(300-x)/1495\). [2]
(b) Using partial fractions, solve for t as a single logarithm involving x. [9]
