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Reducing to straight line Example

Reducing to straight line Example. Two variables a and b are related by the formula s= at c , where a and c are constants. Show that this relationship can be written as : Log s = c logt + loga. S = at c Log S = Log at c

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Reducing to straight line Example

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  1. Reducing to straight lineExample Two variables a and b are related by the formula s=atc, where a and c are constants • Show that this relationship can be written as : • Log s = c logt + loga S = atc Log S = Log atc Log S = Log a + Log tc(using the log law logaxy= loga x + logay) Log S = Log a + c Log t (using the log law logaxk= k loga x ) Log S = c Log t + Log a

  2. (ii) Explain why the model can be tested by plotting log y vs log x Compare Log S = c Log t + Log a With the equation of straight line y = m x + c • Log S = c Log t + Log a should give a straight line if s=atc • where : • y = log S • x = log t • m(gradient) = c • c(intercept) = Log a

  3. (iii) Plot log s vs log t and estimate the values of a and c

  4. This looks very linear to me But I need a carefully drawn graph that I can estimate the values of the gradient and intercept from. So I will use Excel

  5. Log s = c logt + loga C (gradient) = Log a S=atc is data relationship where a = 3.98 and c =0.5 Log a = 0.6  a= 100.6 = 3.98 C = 0.5

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