Final answer:
The equation expressing liters in terms of time assuming an average constant rate of change is L(t) = L0 - r*t, where L0 is the initial volume (unknown in this context) and r is the average rate of change, which is 14.4L/min calculated from the given data.
Step-by-step explanation:
To write an equation expressing liters in terms of time based on the given information where a tub has 38.4, 21.6, and 9.6 liters remaining at 1, 2, and 3 minutes respectively, we can use the points to determine the rate at which the tub is losing water. First, we'll calculate the difference in volume per minute to find the rate:
- From minute 1 to minute 2: (38.4L - 21.6L) / (2min - 1min) = 16.8L/min
- From minute 2 to minute 3: (21.6L - 9.6L) / (3min - 2min) = 12L/min
Note that the rate of water loss is not constant since it changes from 16.8L/min to 12L/min. Therefore, a linear model would not fit this data precisely, and more information might be needed to develop an accurate model. However, if we assume a constant average rate of change, we can calculate it by taking the total change in volume over the total change in time from minute 1 to minute 3:
Average rate of change = (38.4L - 9.6L) / (3min - 1min) = 28.8L / 2min = 14.4L/min
With an average rate of change of 14.4L/min, we can express the equation as L(t) = L0 - r*t where L(t) is the liters remaining at time t, L0 is the initial liters at t=0 (which we don't have), and r is the rate of change. It's important to remember that this equation assumes a constant rate which may not be valid in this context.