The speed, [tex]$s$[/tex], of the current in a certain whirlpool is modeled by [tex]$s=\frac{300}{d}$[/tex], where [tex]$d$[/tex] is the distance from the center of the whirlpool. Which statement is true?
A. As you move closer to the center of the whirlpool, the speed of the current approaches 0.
B. As you move closer to the center of the whirlpool, the speed of the current approaches 1.
C. As you move closer to the center of the whirlpool, the speed of the current approaches infinity.
D. As you move closer to the center of the whirlpool, the speed of the current approaches 300.
Answer (2)
As distance d from the center of the whirlpool approaches 0, the speed of the current s represented by s = d 300 increases without bound. Thus, the speed approaches infinity as you move closer to the whirlpool's center, making option C the correct answer. The behavior can be illustrated by calculating specific values of s for decreasing d .
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The speed of the current in a whirlpool is modeled by s = d 300 .
We analyze the behavior of s as d approaches 0.
As d approaches 0, s approaches infinity.
Therefore, as you move closer to the center of the whirlpool, the speed of the current approaches infinity. $\boxed{c}
Explanation
Understanding the Problem The problem states that the speed, s , of the current in a whirlpool is modeled by the equation s = d 300 , where d is the distance from the center of the whirlpool. We need to determine what happens to the speed s as we move closer to the center of the whirlpool, which means d approaches 0.
Analyzing the Limit To analyze the behavior of the speed s as d approaches 0, we can consider the limit: d → 0 lim d 300 As d gets closer and closer to 0, the fraction d 300 becomes larger and larger. For example, if d = 0.1 , then s = 0.1 300 = 3000 . If d = 0.01 , then s = 0.01 300 = 30000 . If d = 0.001 , then s = 0.001 300 = 300000 .
Determining the Behavior As d approaches 0, the value of s increases without bound. This means that the speed of the current approaches infinity.
Conclusion Therefore, the correct statement is: As you move closer to the center of the whirlpool, the speed of the current approaches infinity.
Examples
Imagine you're designing a system to manage the flow of water in a circular tank. The speed of the water increases as it gets closer to the drain at the center. Understanding this relationship, modeled by s = d 300 , helps you predict how fast the water will move at different distances from the center. This is crucial for designing effective control mechanisms and preventing overflow or damage. This concept applies to various scenarios, such as designing efficient drainage systems, optimizing fluid mixing processes, or even understanding weather patterns like hurricanes.
