SOLUTION: since the beginning of the month, a local reservoir has been losing water in a linear fashion. On the 12th of the month the resrviour held 200 million gallons of water, and on the
Question 160809: since the beginning of the month, a local reservoir has been losing water in a linear fashion. On the 12th of the month the resrviour held 200 million gallons of water, and on the 21st of the month it held only 164 million gallons. Assuming this continues, express the number of gallons as a function of time,t, where t is the number of days elapsed since the beginning of the month. Determine when the tank will be empty. Found 2 solutions by vleith, AksharTech:Answer by vleith(2983) (Show Source): You can put this solution on YOUR website! You are given two points (12,200) and (21,164)
Find the slope million gallons/day
You are asked to express in terms of t, where t is the numbers of days since the beginning of the month. So you want to get a linear equation in the form you have m, you need b. t is the number of days since the beginning of the month
Let's find the point (1,y), that will give you the amount of water on the first of the month. We need to 'go back up the line' 12 days. If we are losing -4 million gallons a day, and we back up 12 days, that says there were 4*12 or 48 million more gallons in the tank on the first of the month.
Add 48 to the amount on day 12 to get (48+200) = 248million gallons.
on day 12, t = 12 and you have 200
on day 21, t = 21 and you have 164
Finally you are asked when the pond is emtpy. At that point, y = 0
You have a little over 2 months from day 1
Answer by AksharTech(1) (Show Source): You can put this solution on YOUR website! 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.
Solve this pair of linear equations.
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. ..... (Answer#1)
Plug-in 0 for the quantity of water in this equation to determine when the tank will be empty.
Therefore the tank will be empty after 62 days. ....(Answer#2)