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.
104 exam-style questions on OCR A Level Maths 1.6 Exponentials and Logarithms, covering 1.6.1 Properties of the exponential function, 1.6.2 Gradient of e^(kx) (A-level only), 1.6.3 Definition of the logarithm, 1.6.4 The natural logarithm function, 1.6.5 ln x as inverse of e^x, 1.6.6 Laws of logarithms, 1.6.7 Equations involving exponentials, 1.6.8 Reduction to linear form, and 1.6.9 Modelling using exponential functions. Each one has a worked solution and a mark scheme showing where the marks go.