Question 645493
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At zero days, there are 168 gallons in the barrel, so a graph of your function on a *[tex \LARGE tg] coordinate plane where points are denoted with ordered pairs of the form *[tex \LARGE \left(t,\,g\right)], must have the point *[tex \LARGE \left(0,\,168\right)] on it.


At one day, there are 168 minus 13 equals 155 gallons in the barrel, so the graph of your function must have the point *[tex \LARGE \left(1,\,155\right)] on it.


Now that you have two points on a graph of your function, you can use the two point form of an equation of a line to model your function:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ g\ -\ g_1\ =\ \left(\frac{g_1\ -\ g_2}{t_1\ -\ t_2}\right)(t\ -\ t_1) ]


where *[tex \Large \left(t_1,g_1\right)] and *[tex \Large \left(t_2,g_2\right)] are the coordinates of the given points.


Just plug in the numbers and then do the arithmetic.  Then arrange your equation so that your have *[tex \LARGE g] by itself in the LHS.


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