Develop a linear interpolation formula for the function e^0.5x using the values at x1 = 0 and x2 =

Question

Develop a linear interpolation formula for the function e^0.5x

Answer 1

Only one value has been provided, so let x₂=ln(4) as an illustration of the method.

y₁=e^0.5x₁ and y₂=e^0.5x₂, so y₁=1 (because x₁=0) and y₂=e^0.5ln(4)=e^ln(√4)=2.

(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁),

(y-1)/x=(2-1)/ln(4), y-1=x/ln(4), y=x/ln(4)+1 is the linear interpolation.

y=0.7213x+1 is the approximate linear interpolation.