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 (MEI) A Level Maths 1.8 Exponentials and Logarithms, covering 1.8.1 The function y = a^x, 1.8.2 Convert between index and logarithmic form, 1.8.3 Logarithm as inverse of exponential, 1.8.4 Laws of logarithms, 1.8.5 Values of log_a a and log_a 1, 1.8.6 Solve equations of the form a^x = b, 1.8.7 Reduce y = ax^n and y = ab^x to linear form, 1.8.8 The function y = e^x, 1.8.9 Gradient of e^kx (A-level only), 1.8.10 The function y = ln x, and 1.8.11 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.