A solution containing a medication is infused intravenously into a patient at a varying rate r(t) milligrams per minute, where t is the time in minutes since the infusion begins. Consider the interval 0≤t≤60.
a. Part 1: (a) Indicate the units of ∫060r(t)dt and describe what this integral represents in the context of the infusion.
b. Part 2: (b) Suppose r(25)=−2.4. Explain what the negative value of r at t=25 minutes implies about the medication movement at that instant.
c. Part 3: (c) If ∫060r(t)dt=200, interpret the meaning of the value 200 in the context of the patient’s treatment.
d. Part 4: (d) Explain how the Fundamental Theorem of Calculus connects the function R(t)=∫0tr(s)ds to the instantaneous rate r(t) within this scenario.