9514 1404 393
Answer:
[-4,3]
Step-by-step explanation:
The domain is the left-right (horizontal) extent of the function. The dots at the end of the continuous line are solid, so the brackets on the interval are square brackets.
The left dot is at x=-4; the right dot is at x=3, so the domain is ...
[-4,3]
(a) Let denote the amount of sugar in the tank at time
. The tank starts with only pure water, so
.
(b) Sugar flows in at a rate of
(0.07 kg/L) * (7 L/min) = 0.49 kg/min = 49/100 kg/min
and flows out at a rate of
(<em>A(t)</em>/1080 kg/L) * (7 L/min) = 7<em>A(t)</em>/1080 kg/min
so that the net rate of change of is governed by the ODE,
or
Multiply both sides by the integrating factor to condense the left side into the derivative of a product:
Integrate both sides:
Solve for :
Given that , we find
so that the amount of sugar at any time is
(c) As , the exponential term converges to 0 and we're left with
or 75.6 kg of sugar.