Question

Consider the concentration C of a drug in the blood as a function of x, the amount of the drug given, and t, the time since the injection. For 0≤x≤2 and t≥0, we have C=f(x,t)=xte^(-3t).

The units of C are milligrams per liter, the units of x are milligrams, and the units of t are hours.
Sketch the following two single-variable functions on a separate page. Pay attention to the domain given at the start of the problem.

a)f(2,t)
b)f(x,1)

Using your graph in (a), where is f(2,t) a maximum? t=?
Using your graph in (a), where is f(2,t) a minimum? t=?
Using your graph in (b), where is f(x,1) a maximum? x=?
Using your graph in (b), where is f(x,1) a minimum? x=?

Answer 1

To sketch the functions C=f(x,t), we can choose specific values of x and t, plot C against t, and analyze the graphs to find maximum and minimum points.

Step-by-step explanation:

To sketch the functions, we can choose specific values of x and t to calculate C. Let's start with part (a), where we need to sketch f(2,t). Plugging in x=2, we have C=f(2,t)=2te^(-3t).

For part (b), we need to sketch f(x,1). Plugging in t=1, we have C=f(x,1)=xe^(-3).

In both cases, we should choose a range for t and plot C against t to obtain the graphs. For example, let's choose t values from 0 to 5 hours. We can use a computer program or calculator to plot these functions. Once the graphs are plotted, we can analyze them to find the maximum and minimum points.