1.4 Graphing 55 93. Drug Absorption After a patient takes the painkiller ac- etaminophen (often sold under the brand name Tylenol), the concentration of drug in their blood increases at first, as the painkiller is absorbed into the blood, and then starts to decrease as the drug is metabolized or removed by the liver. In one study, the concentration of drug (c, measured in μg/ml) was measured in a patient as a function of time (r, measured in hours since the drug was administered). The data in this example is taken from Rowling et al. (1977). 1 c 1 10.61 1.5 8.73 2 763 23 す 56 5.55 3.97 3.01 2.39 (a) You want to determine from the data whether the relation- ship between concentration and time follows a power law c = atb for some set of constants a and b, or whether it instead follows an exponential law for some constants k and d. c = kd' Explain how you could plot the data with transformed horizon- tal and vertical axes to determine which mathematical model is correct. (b) By plotting log c against log in one graph, and logc against r in another, explain why the data supports the second model (ex- ponential decay) better than it supports the first model. (c) From your plot of log c against t, estimate the parameter d.