A study explores the relationship between the basal metabolic rate, RRR (measured in Watts), and the body mass, mmm (measured in kilograms), of various mammals. A graph of log10R\log_{10} Rlog10R against log10m\log_{10} mlog10m is found to be a straight line. Data for two specific mammals are plotted as points on this line: Mammal A at (0.35,1.22)(0.35, 1.22)(0.35,1.22) and Mammal B at (2.75,3.14)(2.75, 3.14)(2.75,3.14).
Find the equation of the straight line in the form
log10R=a+blog10m \log_{10} R = a + b \log_{10} m log10R=a+blog10mwhere aaa and bbb are constants to be found.
Show that R=KmnR = Km^nR=Kmn, where KKK and nnn are constants to be determined.
A different mammal has a basal metabolic rate of approximately 250 Watts. Use your answer to part (a)(ii) to find an estimate for the body mass mmm of this mammal.
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.