The decay of a radioactive substance is modelled using the formula N=1000e−ktN = 1000e^{-kt}N=1000e−kt where N N\,N is the number of atoms after t t\,t years and k k\,k is a positive constant.
Write down the number of atoms when the substance started to decay.
Given that it takes 14.4 years for half of the substance to decay, find the value of k k\,k to 3 significant figures.
Calculate the number of atoms left when t=30t = 30t=30.
62 exam-style questions on AQA A Level Maths 1.9 F: Exponentials and logarithms, covering 1.9.1 Exponential functions and their graphs, 1.9.2 Gradient of e^kx (A-level only), 1.9.3 Logarithms as inverse functions, 1.9.4 Laws of logarithms, 1.9.5 Solving exponential equations, 1.9.6 Logarithmic graphs to estimate parameters (A-level only), and 1.9.7 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.