SOLUTION: 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)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 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)       Log On


   

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.
Found 2 solutions by mananth, MathTherapy:
Answer by mananth(16946) About Me  (Show Source):
Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

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.

%28a%29%2F%281+%2B+be%5E%28-kt%29%29+=+a%2F2

a%281+%2B+be%5E%28-kt%29%29+=+2a ----- Cross-multiplying

1+%2B+be%5E%28-kt%29+=+2a%2Fa

1+%2B+be%5E%28-kt%29+=+2

be%5E%28-kt%29+=+2+-+1

be%5E%28-kt%29+=+1

e%5E%28-kt%29+=+1%2Fb

ln+%281%2Fb%29+=+-+kt

highlight_green%28ln%281%2Fb%29%2F%28-+k%29+=+t%29

Send comments and “thank-yous” to “D” at MathMadEzy@aol.com