A linear model fits a hopper that loses the same number of kilograms each hour. Find the loss per hour from the change in material and the time it took. Then subtract that hourly loss from the starting amount and use a Desmos regression to find when the target remains. Keep time measured from the beginning, not from the later reading.
Hints
- Hint 1
A unit rate is the amount consumed in one hour. Find how many kilograms disappeared between the beginning and the later reading, then divide by the number of hours that passed.
- Hint 2
The question asks for time from the beginning, so call that starting moment time . For any time , subtract the hourly loss times from the original amount.
- Hint 3
Set the remaining amount equal to the target. In Desmos, use for the unknown number of hours and to find the value that makes both sides equal.
Step-by-step
Model the material remaining
Step 1Find the hourly consumption rate
The hopper lost kilograms in hours. A unit rate is the loss in one hour, so type in Desmos. It prints : the line consumes kilograms per hour.
- Step 2
Write the equation for the target amount
Let be the hours since production began. In hours, the line consumes kilograms, so remaining material equals starting material minus material consumed:
Starting with instead would leave out the first hours.
- Step 3
Find the time in Desmos
Type . Here is the unknown time, and tells Desmos to find the value that makes the sides equal. Under PARAMETERS, Desmos reports . So only kilograms remain 7 hours after production began. Choice C.