Question

Solve for ? in the following equation by means of linear interpolation

((1+? )^10 - 1)/? = 25

Answer 1

So given equation is:

Hence we have

Let us write above equation as a function:

i.e.

Put different values of i in above equation

At i=1 , f(i)=998

At i=0.5 , f(i)=44.17

Hence we can take further values with less i as f(i) is decreasing with decreasing i

Let us interpolate more

Take i=0.25, f(i)=2.063

Take i= -0.25, f(i)=5.31

Hence f(i) again increased

Hence interpolation clearly shows that i lies between 0.25 and -0.25

Take i=0

Then f(i)=0

Hence i = 0 is the solution

But i=0 sometimes we refer as diverging solution

But we see i=0.192 also satisfies this eqn

Hence i=0.192 is solution