The concentration of a specific reactant in a chemical solution, C C\,C mg/L, t t\,t hours after the reaction starts, is modelled by the equation:
C=250e−0.12t+15,t≥0 C = 250e^{-0.12t} + 15, \quad t \ge 0 C=250e−0.12t+15,t≥0Determine the initial concentration of the reactant.
Sketch the graph of C C\,C against ttt. On your sketch, state the equation of any asymptote to the curve.
Find the value of t t\,t for which the concentration is 80 mg/L, giving your answer to 2 decimal places.
Show by differentiation that
dCdt=A+BC \frac{dC}{dt} = A + BC dtdC=A+BCwhere A A\,A and B B\,B are constants to be found.
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.