The monthly rate of increase of a fish population in a reservoir is equal to 1.5% of the current population. P P\,P is the population in hundreds and t t\,t is the time in months.
Write down a differential equation for this relationship.
Show that P=Ae0.015tP = Ae^{0.015t}P=Ae0.015t where A A\,A is a constant.
Given that the initial population is 800 fish. Find the population after 2 years (24 months), to the nearest whole number.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
