Respuesta :
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
A 12-gallon container filled with water is being drained at a constant rate of 2 gallons per minute. Where t is the The number off gallons of water,w, in the container t minutes after it begins to drain can be modeled by the equation w=12-2t.
a) Write a formula that express w in terms of t.
b) As t increases from 2 to 5, w varies from __ to ___ ?
c) As t increases from 2 to 5, how much do t and w change by ?
Answer:
a) [tex]w = 12 - 2t[/tex]
b) As t increases from 2 to 5, w varies from 8 to 2 gallons.
c) As t increases from 2 to 5, t changes by 3 and w changes by -6.
Step-by-step explanation:
a) We are given that a 12-gallon container filled with water is being drained at a constant rate of 2 gallons per minute.
Let w represents water and t represents time then we can write,
[tex]w = 12 - 2t[/tex]
Since the water is being drained at rate of 2 gallons per minute that is why we have subtracted the term 2t from the initial capacity of the container that is 12 gallons.
b)
At t = 2
[tex]w = 12 - 2(2)\\\\w = 12 - 4 \\\\w = 8 \: gallons[/tex]
At = 5
[tex]w = 12 - 2(5)\\\\w = 12 - 10 \\\\w = 2 \: gallons[/tex]
Therefore, as t increases from 2 to 5, w varies from 8 to 2 gallons.
c)
change in t
[tex]\Delta t = 5 - 2\\\\\Delta t = 3[/tex]
change in w
[tex]\Delta w = 2 - 8\\\\\Delta w = -6[/tex]
Therefore, as t increases from 2 to 5, t changes by 3 and w changes by -6.
