The annual rate of increase of an investment's value is proportional to its value, specifically 3.5% of the value. V V\,V is the value in thousands of pounds and t t\,t is the time in years.
Write down a differential equation for this relationship.
Show that V=Ae0.035tV = Ae^{0.035t}V=Ae0.035t where A A\,A is a constant.
Given that the initial value of the investment is £12,000. Find the value after 5 years, giving your answer to the nearest £10.
480 exam-style questions on AQA A Level Maths 1.11 H: Integration, 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). Each one has a worked solution and a mark scheme showing where the marks go.