How to linearise y = ax b Demo for Swine Flu CW Using Logs to Linearise Curves

Linearising a power equation using logs y = ax b Swine Flu x y This graph is NOT linear

Linearising a power equation using logs y = ax b y = ax b log y = log (ax b ) log y = log a + logx b log y = log a + blogx log y = blogx + log a So make a new table of values where Y = log y and X = log x This is of the form y = mx + c. Taking logs of both sides log(ab) = log(a) + log(b) log(a x ) = xlog(a) gradient = b y intercept = log a YmXc

x y x=log x y=log y From the graph gradient y intercept m = c =

gradient = m = = b y intercept = c = = log a y = ax b log y = blogx + log a Y = X a = =  10 it = a Forwards and backwards a  log it  YmXc

Using the equation If x = 5.5 find y y = 3.54× = 38.2 Check if the answer is consistent with the table x = 5.5 find y y = 38.2 which is consistent with the table y = 3.54x x y

Using the equation If y = 100 find x 100 = 3.54x log100 = log(3.54x ) = log(3.54)+log(x ) = log(3.54) log(x) y = 3.54x log(ab) = log(a) + log(b) log(a x ) = xlog(a) log both sides

log 100= log(3.54) log(x) Forwards and backwards x  log it  ×  +log3.54 = log 100 log100  –log 3.54  ÷  10 it = x x = x = which is consistent with the table Check if the answer is consistent with the table y = 100 find x x y