The total area, AAA hectares, affected by a wildfire is modelled by the formula
A=abt A = ab^t A=abtwhere aaa and bbb are constants and ttt is the number of days after the fire was first detected at 6:00 AM on Monday. A graph of log10A\log_{10} Alog10A against ttt is plotted for the first 3 days. The data points form a straight line with a gradient of 0.14 and a vertical intercept on the log10A\log_{10} Alog10A axis of 0.85.
Determine the value of aaa and the value of bbb according to the model, rounding your answers to two decimal places.
Provide a practical interpretation of the constant aaa in the context of this model.
Use the model to estimate the area affected by the wildfire at 6:00 AM on the following Saturday.
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.