Question

Find a power function of the form y=ax^p that goes through the points (1,3) and (4,96). Round p to one decimal place.

Answer 1

y = a * x^p

Given the points ( 1 , 3 ) and (4 , 96 )

So, when x = 1 , y = 3

so,

3 = a * (1)^p

so, a = 3

And when x = 4 , y = 96

so,

96 = 3 * 4^p

solve to find p

4^p = 96/3

4^p = 32

Take ln for both sides

p ln 4 = ln 32

p = (ln 32)/(ln 4) = 2.5

so, the equation will be

y = 3 * x^2.5