Burning down the house

Use the conservation equation to find s\langle s\rangle in terms of ρtree,\rho_\textrm{tree}, f,f, and r.r.

What is s\langle s\rangle when ρtree=0.4,\rho_\textrm{tree} = 0.4, f=0.01,f = 0.01, and r=0.05?r = 0.05?


Hint: Recall that ρempty+ρtree+ρburning=1.\rho_\textrm{empty} + \rho_\textrm{tree} + \rho_\textrm{burning} = 1.

Assume that ρburning{ρempty,ρtree}.\rho_\textrm{burning} \ll \{\rho_\textrm{empty}, \rho_\textrm{tree}\}.

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