after 30 seconds, there are 14 gallons of water left in the tub. One minute after you pull the plug, there are 9 gallons left. assume that the numbers of gallons varies linearly with the time since the plug was pulled. what are the two ordered pairs and what is the rate of change per second. please help.
You first must define your ordered pairs.
let my general ordered pair be (time, volume)
secondly, make sure you have the same units, e.b. seconds or minutes.
I would have:
(30,14) and (60,9)
now find the slope, and your answer would be gallons/second
let me know what you get.
6 gallons every second is drained?
nope
rate of draining = (9-14)/(60-30)
= -5/30 gallons/sec
or -1/6 gallons/sec
the negative shows the volume is decreasing or "draining"
remember, slope is (the difference in the y's)/difference in the x's
I think you had it backwards, and also ignored the negative sign
how many gallons of water were in the tub initially before the plug was pulled?
what would be my function equation for the line in the form of y=mx+b
To find the two ordered pairs and the rate of change per second, we can set up a system of linear equations based on the given information.
Let's assume that the time since the plug was pulled is measured in seconds, and let's denote the number of gallons of water left in the tub at time t as W(t).
Given information:
At 30 seconds (t = 30), there are 14 gallons left:
W(30) = 14
One minute after pulling the plug (t = 60), there are 9 gallons left:
W(60) = 9
To find the rate of change per second, we need to determine how much the number of gallons decreases per second, which can be represented by the slope of the linear function.
Now, let's set up the system of linear equations:
Equation 1: W(30) = 14
Equation 2: W(60) = 9
To find the slope (rate of change per second), we need to calculate the difference in the number of gallons between t = 60 and t = 30 (ΔW) and divide it by the difference in time (Δt).
ΔW = W(60) - W(30) = 9 - 14 = -5 gallons (since the number of gallons is decreasing)
Δt = 60 - 30 = 30 seconds
Rate of change per second = ΔW / Δt = -5 gallons / 30 seconds
Simplifying, we find that the rate of change per second is approximately -0.1667 gallons per second.
Finally, the two ordered pairs can be expressed as (t, W(t)):
At t = 30 seconds: (30, 14)
At t = 60 seconds: (60, 9)
Therefore, the two ordered pairs are (30, 14) and (60, 9), and the rate of change per second is approximately -0.1667 gallons per second.