Newton's Method

Question

Round of to 4 decimal places.

Answer 1

NEWTON’S METHOD

Let f(t)=70e⁻¹˙⁵ᵗ+25e⁻⁰˙⁰⁷⁵ᵗ-5,

f'(t)=-105e⁻¹˙⁵ᵗ-1.875e⁻⁰˙⁰⁷⁵ᵗ.

Then, according to Newton’s Method, t=t-f(t)/f'(t) for successive iterations of t.

t₀=21

t₁=21.451356

t₂=21.459170

t₃=21.459172

So the solution to 4 decimal places is t=21.4592.