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Difficulty: EasyLinear and Exponential Growth

An administrator installs a new security update on a computer server. The update is designed to identify and quarantine system errors such that the total number of errors on the server is reduced by 12%12\% each hour. Which of the following best describes the relationship between the time, in hours, since the update was installed and the number of system errors remaining on the server?

  1. Decreasing exponential, because the number of errors decreases by a constant percentage each hour.Answer
  2. B
    Decreasing linear, because the number of errors decreases by a constant quantity each hour.
  3. C
    Increasing exponential, because the number of errors increases by 12%12\% each hour.
  4. D
    Decreasing linear, because the number of errors decreases by exactly 1212 errors each hour.

Answer

Decreasing exponential, because the number of errors decreases by a constant percentage each hour.
The correct answer is the option stating that the relationship is decreasing exponential because the number of errors decreases by a constant percentage each hour. In mathematical modeling, when a quantity changes by a fixed percentage over equal intervals of time, it is modeled by an exponential function. Since the quantity is being reduced, it is a decreasing exponential relationship.

Step-by-Step Solution

1
Analyze the rate of change described in the problem.
The number of system errors is reduced by 12%12\% each hour.
Identifying how the quantity changes per unit of time is key to determining the model type.
2
Distinguish between linear and exponential relationships based on the rate of change.
Since the change is a constant percent decrease (12%12\%) rather than a constant numerical amount, the relationship is exponential rather than linear.
Exponential models represent situations with constant percentage changes, while linear models represent constant absolute changes.
3
Determine the direction of the change (growth or decay).
Because the number of errors is reduced, the quantity is decreasing, representing exponential decay (decreasing exponential).
A reduction in quantity indicates decay (decreasing) rather than growth (increasing).

Key Concept

Linear and Exponential Growth
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Topics

Linear and Exponential Growth

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