It is given that y=ax^{b}, where a and b are constants. The diagram below shows the equation by plotting lgy against lg x. Find the value of a and of b.

Solution:

y=ax^{b}

lg y = lg(y=ax^{b})

lg y = lg a + b(lg x)

Y = mX + C

m=b, C = lg a

b = (o – (-2)) / (1 -0) lg a = -2

b = 2 a =10^{-2 }

a = 1/100