Suppose another drug is administered intravenously. The concentration c of the drug (in mg/L) in the bloodstream, t hours after it is administered, is modeled by the function c(t) = 20t / (t^2 + 4)
a. Determine when the concentration will be 0.5 mg/L.
The concentration will be 0.5 mg/L at t = 39.89, so it will take 40 hours after the drug been administered for it to reach 0.5 mg/L.
b. Complete the table representing the concentration of the drug in the bloodstream, t hours after administration. Round to two decimal places as needed.
t: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
c(t): 0, 5, 4, 3, 2.35, 1.92, 1.62, 1.4, 1.23, 1.10, 1.00
c. What is a reasonable domain for this function? Justify your answer.
The reasonable domain for this function is t ≥ 0. Since the concentration of the drug is 0 at t = 0 and the concentration never actually becomes zero for any t, where t > 0. At any time t, t ≥ 0 there is a concentration c, where c ≥ 0
d. When must the patient receive the next intravenous dose of the drug in order to maintain a concentration above 1 mg/L and below 8 mg/L? Explain your reasoning.
T equals 1.25 hours. The drug has to be administered in between the time where t (1.25≤ t≤ 20) to keep the concentration in between 1 mg/L and 8 mg/L.