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 (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.