The concentration of a drug in an organ at any time (in seconds) is given by where is measured in grams/cubic centimeter How long would it take for the concentration of the drug in the organ to reach 0.17 How long would it take for the concentration of the drug in the organ to reach 0.16 Round your answer to the nearest hundredth.
A)17.31 seconds; 20.30 seconds
B)17.33 seconds; 20.27 seconds
C)17.36 seconds; 20.25 seconds
D)17.32 seconds; 20.31 seconds

Question

The concentration of a drug in an organ at any time  (in seconds) is given by  where  is measured in grams/cubic centimeter  How long would it take for the concentration of the drug in the organ to reach 0.17  How long would it take for the concentration of the drug in the organ to reach 0.16  Round your answer to the nearest hundredth.
A)17.31 seconds; 20.30 seconds 
B)17.33 seconds; 20.27 seconds 
C)17.36 seconds; 20.25 seconds 
D)17.32 seconds; 20.31 seconds

Quizplus · Accepted Answer

To find the time it takes for the concentration of the drug in the organ to reach a certain level, we need to solve the equation given for t.

For 0.17 g/cm³:

0.17 = (140t)/(t² + 9)

0.17t² + 1.53t - 0.17(9) = 0

Using the quadratic formula:

t = (-1.53 ± √(1.53² - 4(0.17)(-1.53)))/(2(0.17))

t ≈ 17.33 seconds or t ≈ -10.60 seconds

Since time can't be negative, we choose t ≈ 17.33 seconds.

Similarly, for 0.16 g/cm³:

0.16 = (140t)/(t² + 9)

0.16t² + 1.44t - 0.16(9) = 0

Using the quadratic formula:

t = (-1.44 ± √(1.44² - 4(0.16)(-1.44)))/(2(0.16))

t ≈ 20.27 seconds or t ≈ -7.94 seconds

Again, since time can't be negative, we choose t ≈ 20.27 seconds.

Rounding to the nearest hundredth, the answer is (B) 17.33 seconds and 20.27 seconds.

The Concentration of a Drug in an Organ at Any