To represent the relationship between the number of minutes since the tub started draining and the amount of water left in the tub, we need to consider the rate at which the water is draining.
Since the tub starts with 40 gallons of water and drains at a constant rate of 8 gallons per minute, the equation for the amount of water \( W \) in the tub after \( t \) minutes is:
\[ W(t) = 40 - 8t \]
This is a linear equation with a negative slope, meaning the amount of water decreases linearly over time.
To determine key points:
- At \( t = 0 \) minutes: \( W(0) = 40 \) gallons
- At \( t = 1 \) minute: \( W(1) = 40 - 8 \times 1 = 32 \) gallons
- At \( t = 2 \) minutes: \( W(2) = 40 - 8 \times 2 = 24 \) gallons
- At \( t = 3 \) minutes: \( W(3) = 40 - 8 \times 3 = 16 \) gallons
- At \( t = 4 \) minutes: \( W(4) = 40 - 8 \times 4 = 8 \) gallons
- At \( t = 5 \) minutes: \( W(5) = 40 - 8 \times 5 = 0 \) gallons
This results in a straight-line graph that starts at (0, 40) and goes down to (5, 0).
Now, let's look at the responses:
- The first option describes a concave upward curve, which is incorrect for a linear decrease.
- The second option describes a concave downward curve, which is also incorrect.
- The third option shows a straight line connecting the points (0, 40) and (5, 0). This correctly represents the linear decrease in water volume over time.
- The fourth option starts at (8, 0) and (0, 40), which does not fit the situation since it suggests 8 minutes lead to 0 gallons, which isn't correct based on our findings.
Thus, the correct choice is the third option, which shows a straight line between (0, 40) and (5, 0).
1 answer