The concentration of a drug in an organ at any time t (in seconds) is given by where x(t) is measured in grams/cubic centimeter .Sketch the graph of x.

Question

The concentration of a drug in an organ at any time t (in seconds) is given by  where x(t) is measured in grams/cubic centimeter  .Sketch the graph of x.

Quizplus · Accepted Answer

The graph of x will be an exponential curve because of the e^(b*t) term. The coefficient 11 in front of the expression can be ignored as it only scales the graph vertically. Therefore, the only factor that affects the shape of the curve is the exponent b. To determine which choice is best, we need to consider the behavior of the graph as t increases.

Choice A has a negative exponent (b = -0.1) which means that as t increases, the term e^(-0.1*t) gets smaller and smaller. This corresponds to a decreasing concentration of the drug in the organ over time. This is a plausible scenario for a drug that is cleared from the body over time.

Choice B also has a negative exponent (b = -1) but the magnitude is much larger than in choice A. This means that the drug concentration will decrease much more rapidly over time. This situation is not very realistic as most drugs take some time to be eliminated from the body.

Choice C has a positive exponent (b = 0.1) which means that as t increases, the term e^(0.1*t) gets larger and larger. This corresponds to an increasing concentration of the drug in the organ over time. This situation is also not very realistic as most drugs are metabolized and eliminated from the body over time.

Therefore, choice A is the best choice as it corresponds to a plausible scenario for the behavior of drug concentration in an organ over time.

The Concentration of a Drug in an Organ at Any