The concentration of a drug (C C\,C mg/L) in a patient's bloodstream t t\,t hours after administration is recorded in the table below.
| ttt | 1 | 2 | 4 | 6 | 8 | 10 |
| CCC | 26.3 | 19.1 | 10.0 | 5.2 | 2.8 | 1.4 |
The data is coded using the changes of variable x=tx = tx=t and y=log10Cy = \log_{10} Cy=log10C.
The regression line of y y\,y on x x\,x is found to be y=1.56−0.14xy = 1.56 - 0.14xy=1.56−0.14x.
Given that the data can be modelled by an equation in the form C=abtC = ab^tC=abt where a a\,a and b b\,b are constants, find the values of a a\,a and b b\,b to 3 significant figures.
Give an interpretation of the constant a a\,a in this equation.
Explain why this model might not be reliable for calculating the concentration after 72 hours.
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.