# reduction of a relationship to a linear law

• May 6th 2009, 12:14 AM
scouser
reduction of a relationship to a linear law
y= k(x+1) to the power of n
find approximate values for k and n given that

x 4 8 15
y 4.45 4.60 4.8
• May 6th 2009, 02:57 AM
Logs
Hello scouser
Quote:

Originally Posted by scouser
y= k(x+1) to the power of n
find approximate values for k and n given that

x 4 8 15
y 4.45 4.60 4.8

Take logs of both sides:

$\log y = \log\Big(k(x+1)^n\Big)$

$= \log k +n\log(x+1)$

Plot the graph of $\log y$ against $\log(x+1)$, using the three pairs of values you're given. Draw the best straight line and read off the gradient and intercept.

Gradient = $n \approx 0.065$

Intercept = $\log k$, which gives $k \approx 4$