The rate of decrease in temperature of water in a kettle t t\,t minutes after it switches off is given by:
dθdt=−k(θ−20) \frac{d\theta}{dt} = -k(\theta - 20) dtdθ=−k(θ−20)Where θ \theta\,θ is the temperature of the water in degrees Celsius and k k\,k is a constant to be found.
Given that when t=0t = 0t=0, θ=68\theta = 68θ=68 and when t=2t = 2t=2, θ=44\theta = 44θ=44
Show that
ln(θ−20)=−kt+c \ln(\theta - 20) = -kt + c ln(θ−20)=−kt+c.
Find a model for θ \theta\,θ in the form θ=Ae−kt+B\theta = Ae^{-kt} + Bθ=Ae−kt+B, stating the values of AAA, B B\,B and kkk.
864 exam-style questions on Edexcel A Level Maths Integration, 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. Each one has a worked solution and a mark scheme showing where the marks go.