When Daughter Activity Becomes Equal To Parent Activity

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The discussion revolves around solving a transient equilibrium problem involving exponential functions, specifically the equation e^-0.0495t = 0.0289/(0.0289 - 0.0495)^(e^-0.0495t - e^-0.0289t). The user struggles with the order of operations and the correct application of logarithmic properties. Assistance is provided by another forum member, Thetes, who suggests distributing terms and moving like terms to facilitate taking the natural logarithm. The correct solution to the problem is identified as 26 minutes.

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Hi. New here (Again). I'm having trouble with solving transient equilibrium problem



e-0.0495t= 0.0289 (e-0.0495t- e-0.0289t)
_____________
0.0289-0.0495

I know the answer but can't seem to make this work. Maybe I'm messing up my order of op.
 
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Greetings,

I can't tell if that quantity below the problem is part of the divisor or just something extra, but distribute the quantity into the right side of the equation. Then move the term with the same exponent over to the left. Now you can take the natural log of both sides. Just needed some finessing.
 
I'm sorry. The problem didn't display as typed. Ill try this way. Its:

e^-0.0495t=0.0289/0.0289-0.0495^(e-0.0495t - e-0.0289t)


Thank you Thetes for your assistance. The answer is 26 minutes but I cannot seem to solve and arrive at this value. What am I doing wrong?
 
Last edited:

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