The population of people in a town is modelled using the formula P=a(10bt)P = a(10^{bt})P=a(10bt) where t t\,t is the time in years since 2001, and a a\,a and b b\,b are constants.
Explain what the value of a a\,a represents
In 2008 the population of the town was 54 000. In 2013 the population of the town was 59 000. Use the data to calculate the value of a a\,a and the value of bbb.
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.