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1.8 Exponentials and Logarithms

1.8 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

1.8 Exponentials and Logarithms Questions

  1. A Level
  2. /Maths
  3. /1.8 Exponentials and Logarithms

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.

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