Lets first solve the exponential equation[tex] \frac{400}{1+e^{-x} } =350[/tex] algebraically:
[tex]400=350(1+e^{-x} )[/tex]
[tex]400=350+350e^{-x} [/tex]
[tex]50=350e^{-x} [/tex]
[tex]350e ^{-x} =50[/tex]
[tex]e^{-x} = \frac{50}{350} [/tex]
[tex]e ^{-x} = \frac{1}{7} [/tex]
[tex]ln(e ^{-x} )=ln( \frac{1}{7} )[/tex]
[tex]-x=ln( \frac{1}{7} )[/tex]
[tex]x=-ln( \frac{1}{7} )[/tex]
[tex]x=1.95[/tex]
Now to find the solution using a graphing utility, just type the equation and look for the point in which the graph intercepts the x-axis as shown in the picture. The point in which the graph intercepts the x-axis is a zero of the function, and therefore the solution.
