The concentration CCC (in mg/L) of a bioactive compound in a chemical reactor is modelled by the equation
C=pqt C = pq^t C=pqtwhere ppp and qqq are constants and ttt is the time in hours since the reaction began.
The relationship between ttt and log10C\log_{10} Clog10C is linear. The graph of this relationship passes through the vertical intercept (0,1.48)(0, 1.48)(0,1.48) and the point (25,0.73)(25, 0.73)(25,0.73).
Find an equation for this line in the form log10C=mt+c\log_{10} C = mt + clog10C=mt+c.
Find the value of ppp and the value of qqq, giving your answers to 3 significant figures.
According to the model, find the value of ttt when the concentration reaches 10 mg/L.
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.