The population of bacteria is being measured. The equation log10P=0.5t+1.398\log_{10}P = 0.5t + 1.398log10P=0.5t+1.398 is used to model the population of bacteria, PPP, t t\,t hours after it was first recorded.
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 give 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. Give your answer to 2 significant figures.
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.
