Question

Solve the exponential equation algebraically and use a graphing utility
400/1+e^-x= 350

Answer 1

Lets first solve the exponential equation
`(400)/(1+e^(-x) ) =350` algebraically:

`400=350(1+e^(-x) )`

`400=350+350e^(-x)`

`50=350e^(-x)`

`350e ^(-x) =50`

`e^(-x) = (50)/(350)`

`e ^(-x) = (1)/(7)`

`ln(e ^(-x) )=ln( (1)/(7) )`

`-x=ln( (1)/(7) )`

`x=-ln( (1)/(7) )`

`x=1.95`

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.