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.
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.