Answered

The speed, $s$, of the current in a certain whirlpool is modeled by $s=\frac{300}{d}$, where $d$ is the distance from the center of the whirlpool. Which statement is true?


AAs you move closer to the center of the whirlpool, the speed of the current approaches 0.
BAs you move closer to the center of the whirlpool, the speed of the current approaches 1.
CAs you move closer to the center of the whirlpool, the speed of the current approaches infinity.
DAs you move closer to the center of the whirlpool, the speed of the current approaches 300.

Verified Answer :

  • Identify the speed function as \(s(d) = \frac{300}{d}\).
  • Analyze the behavior as \(d \to 0^+\) by observing that as the denominator approaches zero, the value of the expression increases without bound.
  • Determine that the limit \(\lim_{d \to 0^+} \frac{300}{d} = \infty\).
  • Select the statement: \(\boxed{\text{As you move closer to the center of the whirlpool, the speed of the current approaches infinity.}}\)

Explanation

  1. Problem Analysis and Objective

The speed \(s\) of the current in a whirlpool is modeled by the function \(s(d) = \frac{300}{d}\), where \(d\) is the distance from the center of the whirlpool. We want to understand what happens to the speed as we move closer to the center, which corresponds to the distance \(d\) approaching zero from the positive side (since distance cannot be negative, \(d > 0\)). This is equivalent to finding the limit: \[\lim_{d \to 0^+} \frac{300}{d}\]

  1. Evaluating the Limit

To evaluate \(\lim_{d \to 0^+} \frac{300}{d}\), consider the behavior of the fraction as the denominator \(d\) becomes smaller and smaller. As \(d\) gets closer to 0 through positive values (e.g., \(d = 0.1, 0.01, 0.001, \dots\)), the value of the expression \(\frac{300}{d}\) becomes increasingly large (e.g., \(\frac{300}{0.1} = 3000, \frac{300}{0.01} = 30000, \frac{300}{0.001} = 300000, \dots\)). Since the value increases without bound, the limit is infinity: \[\lim_{d \to 0^+} \frac{300}{d} = \infty\]

  1. Conclusion and Final Answer

Based on our analysis, as the distance \(d\) approaches 0, the speed of the current increases without limit. Therefore, the statement "As you move closer to the center of the whirlpool, the speed of the current approaches infinity" is the correct one.

Examples

In meteorology, the wind speed near the center of a tornado can be modeled by similar inverse functions where the velocity increases as one approaches the eye of the storm. Understanding how values behave near points of discontinuity—like finding that speed approaches infinity—is essential for safety protocols and structural engineering, as it helps determine the extreme conditions that buildings or aircraft must be designed to withstand.

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