The population of bacteria, PPP, is modelled t t\,t hours after it was first recorded by the relationship log10P=0.5t+1.398\log_{10} P = 0.5t + 1.398log10P=0.5t+1.398
Show that P=abtP = ab^tP=abt, where a a\,a and b b\,b are constants to be found. Give the value of a a\,a to the nearest whole number and the value of b b\,b to 3 significant figures.
Interpret the meaning of the constant a a\,a in this model.
Find the population of the bacteria after 10 hours, giving your answer to 2 significant figures.
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.