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 it takes 14.4 years for half of the substance to decay, find the value of k k\,k to three significant figures.
Calculate the number of atoms left when t=30t=30t=30.
Practise AQA A Level Maths 1.9 F: Exponentials and logarithms with exam-style questions for A Level Maths. 37 questions 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, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
