solve for t: 5=12.4te^(-.2t)

Question

Sove for t: 5=12.4te^(-.2t)

Answer 1

5=12.4te^-0.2t.

Let f(t)=12.4te^-0.2t-5.

f'(t)=12.4e^-0.2t+12.4t(-0.2e^-0.2t)=12.4e^-0.2t(1-0.2t).

Iterative method (Newton):

t_n+1=t_n-f(t_n)/f'(t_n), where t₀=1.

t₁=0.4032..., t₂=0.44006..., t₃=0.4403..., t₄=0.44034848066, t₅=t₄.

Therefore t converges to t=0.44035 approx.