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 $0.045$ , $(cancel(0.045)t)/(cancel(color(red)(0.045)))=ln(400)/color(red)(0.045)$

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

How do you solve 4e^(0.045t)<16004e^(0.045t)<1600?