The greatest loss rate estimates are 4,200,000 gallons per day since the start of the spill, but after 44 days about 1,050,000 gallons were diverted into collection tankers.( The remaining amount was lost in the Gulf). Based on these data (assuming that the rate of loss was constant at 4,200,000 gallons per day), write an equation to determine the gallons per day (g) lost after the first 44 days; let d represent the total number of days since the start of the spill, and give the real- world domain for this equation
To determine the gallons per day lost after the first 44 days, we can set up an equation using the given data.
Let's define a variable g as the gallons per day lost after the first 44 days. Since the rate of loss is assumed to be constant at 4,200,000 gallons per day, we can express the total loss in terms of g and d.
The total loss, T, after d days can be calculated by subtracting the amount diverted into collection tankers from the estimated loss:
T = 4,200,000 * d - 1,050,000
This equation represents the total number of gallons lost after d days.
To determine the gallons per day lost after the first 44 days, we need to find the rate of loss per day, which is represented by g. Since the first 44 days have already passed, we subtract 44 from the total number of days to get the number of days after the first 44:
d - 44
Thus, the equation to determine the gallons per day lost after the first 44 days is:
g = (4,200,000 * (d - 44) - 1,050,000) / (d - 44)
The real-world domain for this equation would depend on the specific context of the problem. Usually, it would be appropriate to consider a positive domain for the number of days after the first 44 (d - 44 > 0) and a non-zero domain for the gallons per day lost (g ≠ 0).