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Home Q & A Board Science-Related Homework Help Mathematics
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lialeee lialeee
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11 years ago
Solve for t in the following equation, exactly if possible (don't calculate out an approximate value).

55e^0.571t = 28e^0.794t

I'd appreciate a step-by-step response.  Thanks.
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#1
11 years ago
55 e^(0.571t) = 28 e^(0.794t)
55/28 = e^(0.794t) /  e^(0.571t)
55/28 = e^(0.794t - 0.571t)
55/28 = e^(0.224t)
ln(55/28) = (0.224t)
t = ln(55/28) / 0.224
wrote...
#2
11 years ago
Begin by taking the natural log of both sides:

ln(55e^.571t) = ln(28e^.794t)

Simplify and solve for t:

ln(55) + ln(e^.571t) = ln(28) + ln(e^.794t)
ln(55) + .571t = ln(28) + .794t
ln(55) - ln(28) = .223t
ln(55/28)/.223 = t
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