The annual rate of increase of a population is equal to 2% of the size of the population. y y\,y is the population in millions and t t\,t is the time in years.
Write down a differential equation for this relationship
Show that y=Ae0.02ty = Ae^{0.02t}y=Ae0.02t where A A\,A is a constant
Given that the initial population is 2.5 million. Find the population after 10 years.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
