A researcher is investigating the relationship between the distance from a sound source, x x\,x metres, and the measured intensity of the sound, y y\,y units.
The researcher measures 15 different distances and finds the product moment correlation coefficient between distance and sound intensity to be -0.48.
Using a 5% level of significance, test whether or not there is evidence of a negative correlation between distance and sound intensity. State your hypotheses clearly.
The researcher codes the data using m=log10xm = \log_{10}xm=log10x and n=log10yn = \log_{10}yn=log10y and obtains the model n=3.62−1.95mn = 3.62 - 1.95mn=3.62−1.95m.
The product moment correlation coefficient for the coded data is -0.98.
Explain why this supports the researcher's choice of a non-linear model.
Show that the relationship between x x\,x and y y\,y can be written in the form y=axby = ax^by=axb where a a\,a and b b\,b are constants to be found.
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.