How do you solve #4e^(0.045t)<1600#?

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Answer 1 · 2017-07-26T22:21:57

#t=(200ln(400))/9#

First, we divide both sides by #4# to isolate the #e^(0.045t)#.

#(cancel(4)e^(0.045t))/cancel(color(red)(4))=1600/color(red)(4)=400#

#e^(0.045t)=400#

To remove the #e#, we take the #ln# of both sides: #ln(e^(ax))=ax#

#cancel(ln)(cancel(e)^(0.045t))=ln(400)#

#0.045t=ln(400)#

Now, we nust divide both sides by #0.045#, #(cancel(0.045)t)/(cancel(color(red)(0.045)))=ln(400)/color(red)(0.045)#

#t=ln(400)/0.045=(200ln(400))/9#