The hourly rate of increase of a bacteria colony is equal to 5% of the current size of the colony. N N\,N is the number of bacteria in thousands and t t\,t is the time in hours.
Write down a differential equation for this relationship.
Show that N=Ae0.05tN = Ae^{0.05t}N=Ae0.05t where A A\,A is a constant.
Given that the initial number of bacteria is 4000. Find the number of bacteria after 8 hours to 3 significant figures.
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.
