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.
104 exam-style questions on OCR (MEI) A Level Maths 1.8 Exponentials and Logarithms, covering 1.8.1 The function y = a^x, 1.8.2 Convert between index and logarithmic form, 1.8.3 Logarithm as inverse of exponential, 1.8.4 Laws of logarithms, 1.8.5 Values of log_a a and log_a 1, 1.8.6 Solve equations of the form a^x = b, 1.8.7 Reduce y = ax^n and y = ab^x to linear form, 1.8.8 The function y = e^x, 1.8.9 Gradient of e^kx (A-level only), 1.8.10 The function y = ln x, and 1.8.11 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.