Question 160809
Since the reservoir has been losing water in a LINEAR fashion, the expresion of the function will be similar to the equation of a straight line.
Standard equation of a straight line is as follows:
y = mx + C

Replace y by the quantity of water and x by the time elapsed i.e. 't'.
quantity of water = mt + C   ......(eq-1)

You get two equations by plugging the values provided in the question for Quantity of water and time elapsed.
{{{200=m*12+C}}}
{{{164=m*21+C}}}

Solve this pair of linear equations.
*[invoke linear "m", "C", 12, 1, 200, 21, 1, 164]

You get m = -4 and C = 248
Plug-in these values in eq-1 shown above. So you get the number of gallons as a function of time,t.
{{{QuantityOfWater = -4*t + 248}}}   ..... (Answer#1)

Plug-in 0 for the quantity of water in this equation to determine when the tank will be empty.
{{{0=-4*t+248}}}
{{{4*t=248}}}
{{{t=248/4}}}
{{{t=62}}}
Therefore the tank will be empty after 62 days. ....(Answer#2)