Question 682451

Please help. I need to solve this equation for t and I have no clue on how to do it. If you could please show the steps I would appreciate it very much.

(a)/(1+be^-kt)= (a/2)

This equation is asking for the time t at which the population size will be equal to half of its maximum (a/2). I need to solve for t.


{{{(a)/(1 + be^(-kt)) = a/2}}}


{{{a(1 + be^(-kt)) = 2a}}} ----- Cross-multiplying


{{{1 + be^(-kt) = 2a/a}}}


{{{1 + be^(-kt) = 2}}}


{{{be^(-kt) = 2 - 1}}}


{{{be^(-kt) = 1}}}


{{{e^(-kt) = 1/b}}}


{{{ln (1/b) = - kt}}}


{{{highlight_green(ln(1/b)/(- k) = t)}}}


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