Question

alfred gets into an elevator on the fourth floor. the wires pull up the elevator at a rate of 17 meters per second. the fourth floor is 18 m off the ground level. which equation describes the alfreds height off the ground level as a function of time?

\\(h = 35t\\)
\\(h = 17t + 18\\)
\\(h = 18t + 17\\)
\\(h = 17t\\)

Explanation:

Identify the initial value

The problem states that Alfred starts on the fourth floor, which is \(18\text{ m}\) off the ground level. This represents the initial height when time \(t = 0\). Thus, the vertical intercept (or initial value) is \(18\).

Identify the rate of change

The elevator is pulled up at a rate of \(17\text{ meters per second}\). Since the elevator is moving upward, this rate of change is positive. Thus, the slope (or rate of change) is \(17\).

Formulate the linear equation

Using the slope-intercept form of a linear equation, \(y = mx + b\), we can write the height \(H\) as a function of time \(t\):

$$H = 17t + 18$$

Answer:

• (A) \(H = 35t\)
• (B) \(H = 17t + 18\) (Correct answer)
• (C) \(H = 18t + 17\)
• (D) \(H = 17t\)