The population of bacteria is being measured. The equation log10P=0.301t+1.301\log_{10}P = 0.301t + 1.301log10P=0.301t+1.301 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.
277 exam-style questions on Edexcel A Level Maths Exponentials and Logarithms, covering 14.1 Exponential Functions, 14.2 y = e^x, 14.3 Exponential Modelling, 14.4 Logarithms, 14.5 Laws of Logarithms, 14.6 Solving Equations using Logarithms, 14.7 Working with Natural Logarithms, and 14.8 Logarithms and Non-Linear Data. Each one has a worked solution and a mark scheme showing where the marks go.