After pulling the plug from a tub the amount of water in the

After pulling the plug from a tub, the amount of water in the tub changed at a constant rate of -1.6 gallons per minute. After draining for 3.1 minutes, there were 42 gallons of water remaining in the tub.

A) Find the change in the number of gallons in the tub when the number of minutes the tub has been draining changes from 0 minutes to 6 minutes.

B) How many gallons of water were in the tub before the tub began to drain?

C) Write a formula that determines the number of gallons in the tub, y, in terms of the number of minutes elapsed since the plug was pulled, x.

Solution

a)the amount of water in the tub changed at a constant rate of -1.6 gallons per minute.

after 6 minutes, change in no. of gallons = 1.6*6 = 9.6 galons

b) Lets find th equation hat determines the number of gallons in the tub, y, in terms of the number of minutes elapsed since the plug was pulled, x.

slope = -1.6 point ( 3.1 , 42 gallons)

So, y = -1.6x +c .find c

42 = -1.6*3.1 +c ----> c = 46.96 gallons

So, y = -1.6x +46.96

It means at strating therer were 46.96 gallons of water in tub

c) y = -1.6x +46.96