Question 344067
<font face="Garamond" size="+2">


And I'll bet you can imagine just how frustrating it is for me to read your post when you misspell 'frustrating'.  So depressing, discouraging, disheartening, and disconcerting.  Ah well, perhaps someday you will grow up enough to have the courtesy to proofread your written communications before you send them.


Let *[tex \Large x] represent the number of miles traveled.


Then:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C_1(x)\ =\ 0.24x\ +\ 15]


Represents the total cost in dollars of renting from Company #1 for *[tex \Large x] miles.


Whereas:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C_2(x)\ =\ 0.14x\ +\ 29]


Represents the total cost in dollars of renting from Company #2 for *[tex \Large x] miles.


Clearly, for small values of *[tex \Large x], *[tex \Large \ \ C_1] is less expensive.  Substitute 1 mile for *[tex \Large x] in each of the functions and see which is smaller, i.e. less expensive.


Also, for large values of *[tex \Large x], *[tex \Large \ \ C_2] becomes less expensive at some point.  Substitute 1000 for *[tex \Large x] in each of the functions and see which is smaller, i.e. less expensive.


Somewhere between 1 mile and 1000 miles is a point where the cost of both becomes equal.  This is called the break-even point.  Mileage below the breakeven point makes *[tex \Large C_1] less, above the breakeven point makes *[tex \Large C_2] less.


The breakeven point is where the two costs are equal:



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C_1(x)\ =\ C_2(x)]


But we can replace each side of this equation with the expressions they are equal to:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 0.24x\ +\ 15\ =\ 0.14x\ +\ 29]


Solve for *[tex \Large x].


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
<img src="http://www.evolvefish.com/fish/media/E-FlyingSpaghettiEmblem.gif">
</font>