Question

what happens to the value of the expression 3e as e increases?
choose 1 answer:
a it increases.
b it decreases.
c it stays the same.

Explanation:

Step1: Analyze the expression \(3e\)

The expression \(3e\) represents a product where \(3\) is a constant coefficient and \(e\) is a variable. In a linear relationship of the form \(y = kx\) (here \(y = 3e\), \(k = 3\), \(x = e\)), when the coefficient \(k\) is positive (and \(3>0\)), as the variable \(x\) (or \(e\) in this case) increases, the value of \(y\) (or \(3e\)) will also increase. For example, if \(e = 1\), \(3e=3\times1 = 3\); if \(e = 2\), \(3e = 3\times2=6\); as \(e\) goes from \(1\) to \(2\) (increases), \(3e\) goes from \(3\) to \(6\) (also increases).

Step2: Evaluate the options

• Option A: "It increases" is consistent with the analysis of the linear relationship \(3e\) where the coefficient is positive. As \(e\) increases, multiplying it by a positive constant (\(3\)) will result in a larger value for \(3e\).
• Option B: "It decreases" is incorrect because a positive coefficient times an increasing variable will not decrease.
• Option C: "It stays the same" is incorrect because the value of \(e\) is changing, and since \(3\) is a non - zero constant, the product \(3e\) will change as \(e\) changes.

Answer:

A. It increases.