1. Reducing to straight line Example
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 loga xy= loga x + loga y)
Log S = Log a + c Log t (using the log law loga xk= 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 c9 13 16 18 20 22 t 5 10 15 25 30
log s
0.954
1.114
1.204
1.255
1.301
1.342
log t
0.699
1.0
1.176
1.398
1.477

4. log s
0.954
1.114
1.204
1.255
1.301
1.342
log t
0.699
1.0
1.176
1.398
1.477
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= =
C = 0.5