Question 334509
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Let *[tex \Large x] represent the number of months that she has been in business.


Since it costs her $175 per month, but she has $420 revenue per month, her net income is $245.  So her profit, after *[tex \Large x] months is *[tex \Large 245x] from which you need to subtract the initial $3000 expense.  We want this to be greater than or equal to zero, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 245x\ -\ 3000\ \geq\ 0]


Just solve for *[tex \Large x] and then select the next higher integer, presuming that she accounts for a given month at the end of that month.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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