The population of people in a town is modelled using the formula P=a(10bt)P = a\left(10^{bt}\right)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 00054\,00054000, and in 2013 the population was 59 00059\,00059000. Use this data to calculate the value of a a\,a and the value of bbb, giving your answers to 3 significant figures.
104 exam-style questions on OCR A Level Maths 1.6 Exponentials and Logarithms, covering 1.6.1 Properties of the exponential function, 1.6.2 Gradient of e^(kx) (A-level only), 1.6.3 Definition of the logarithm, 1.6.4 The natural logarithm function, 1.6.5 ln x as inverse of e^x, 1.6.6 Laws of logarithms, 1.6.7 Equations involving exponentials, 1.6.8 Reduction to linear form, and 1.6.9 Modelling using exponential functions. Each one has a worked solution and a mark scheme showing where the marks go.