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1.6 Exponentials and Logarithms

1.6 Exponentials and Logarithms

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Question 16

The variables x x\,x and y y\,y are recorded and the results are shown in the table below

xxx12345678910
yyy4297548711119247826533050327954707439

The data is coded using the changes of variable r=xr = xr=x and s=log⁡10ys = \log_{10} ys=log10​y

a.

The product moment correlation coefficient for the coded data is 0.98 Comment on r r\,r for this model and therefore justify the use of a model in the form y=abxy = ab^xy=abx where a a\,a and b b\,b are constants

[3]
b.

The regression line of r r\,r on s s\,s is found to be s=2.60+0.127rs = 2.60 + 0.127rs=2.60+0.127r

Find the values of a a\,a and bbb, give your answers to 3 significant figures

[3]
Markscheme

1.6 Exponentials and Logarithms Questions

  1. A Level
  2. /Maths
  3. /1.6 Exponentials and Logarithms

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.

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