The population of bacteria is modelled by the equation P=abtP = ab^tP=abt, where a=40a = 40a=40 and b=100.5b = 10^{0.5}b=100.5, t t\,t hours after it was first recorded.
Show that log10P=ct+d\log_{10}P = ct + dlog10P=ct+d, where c c\,c and d d\,d are constants to be found. Give the value of d d\,d to 3 decimal places.
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.