A cab company offers a special discount on fare to senior citizens. The following expression models the average amount a cab driver of the company earns:

[tex]\[

\frac{189x}{x+4} + 250

\][/tex]

What does the constant term in the above expression represent?

A. The constant 250 represents the average amount the company pays a cab driver on a particular day.

B. The constant 250 represents the average amount a cab driver collects on a particular day when no senior citizens travel by the company's cabs.

C. The constant 250 represents the number of senior citizens who travel by the company's cabs.

D. The constant 250 represents the maximum amount a cab driver collects on a particular day when [tex]$x$[/tex] senior citizens travel by the company's cabs.

We start with the expression

[tex]$$
\frac{189x}{x+4} + 250.
$$[/tex]

The term that involves [tex]$x$[/tex] (i.e., [tex]$\frac{189x}{x+4}$[/tex]) accounts for the additional amount the driver collects when senior citizens travel. To understand the significance of the constant term [tex]$250$[/tex], we can evaluate the expression when there are no senior citizens riding the cab, that is, when [tex]$x = 0$[/tex]. Plugging in [tex]$x = 0$[/tex] gives

[tex]$$
\frac{189 \cdot 0}{0+4} + 250 = \frac{0}{4} + 250 = 0 + 250 = 250.
$$[/tex]

This calculation tells us that when no senior citizens are in the cab, the average amount collected by the cab driver is [tex]$250$[/tex].

Thus, the constant [tex]$250$[/tex] represents the average amount a cab driver collects on a particular day when no senior citizens travel by the company's cabs.

Therefore, the correct answer is:

[tex]$$\textbf{R. The constant }250\textbf{ represents the average amount a cab driver collects on a particular day when no senior citizens travel by the company's cabs.}$$[/tex]