How do you solve #(1/4) e^(-2 t) = 0.1#?

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Answer 1 · 2016-02-04T15:29:18

#t=0.458145#

Start from the given equation

#(1/4)*e^(-2t)=0.1#

#4*(1/4)*e^(-2t)=4(0.1)# Multiply both sides by #4#

#e^(-2t)=0.4#

#ln e^(-2t)=ln 0.4# Take the logarithm of both sides

#-2t=ln 0.4#

#(-2t)/-2=(ln 0.4)/-2# Divide both sides by #-2#

#(cancel(-2)t)/cancel(-2)=(ln 0.4)/-2#

#t=(ln 0.4)/-2#

#t=0.458145#

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