Question
You collect data for the elimination of contaminant X from bobwhite quail. When plotted as the natural log of concentration (mg·g−1) versus time (day), the data produce a straight line. You do linear regression on these data, producing the following model: Ln Concentration = 3.50 − 0.29*Time. a. What is the elimination rate constant for contaminant X from quail? b. How long would it take for 50% of contaminant X to be eliminated from a quail? What was the concentration of contaminant X in the study quail at time = 0?
Ans
a. The elimination rate constant for contaminant X from quail can be determined by examining the coefficient associated with the time variable in the linear regression model. In this case, the coefficient is -0.29. The elimination rate constant (k) can be obtained by taking the exponent of this coefficient, as it represents the rate of decrease in the natural log of concentration over time:
k = e^(-0.29)
Using the value of k, you can calculate the elimination rate constant.
b. To determine the time required for 50% of contaminant X to be eliminated from a quail, you can use the elimination rate constant (k) obtained in part a. The half-life (t1/2) of the elimination process can be calculated using the following formula:
t1/2 = ln(2) / k
Substituting the value of k, you can find the time it would take for 50% of the contaminant to be eliminated.
c. To determine the concentration of contaminant X in the study quail at time = 0, you need to substitute the time variable (t) with 0 in the given linear regression model:
Ln Concentration = 3.50 - 0.29 * 0
Simplifying the equation, you find:
Ln Concentration = 3.50
To obtain the concentration (C) at time = 0, you can take the inverse of the natural log (e^x) of both sides:
C = e^(3.50)
Evaluating this expression will give you the concentration of contaminant X in the study quail at time = 0.