Math Problem Statement

The graph of a function models the percentage of charge C in a phone battery over a period of time t, in hours. Based on the graph, which of the following collections of statements about the function and scenario is accurate?

Solution

The correct answer to this question based on the given graph is:

Option D

"The function is always decreasing. As time increases, the charge of the battery is always decreasing. The charge is decreasing at different rates at different times."

Explanation:

  • The graph shows a monotonically decreasing function (it is always decreasing).
  • The rate of decrease is not constant, as evidenced by the curve's varying steepness. The function decreases faster initially and then slows down, showing different rates of change over time.
  • Options A and B are incorrect because they state the charge sometimes increases, which does not occur in the graph.
  • Option C is incorrect because it says the charge decreases at the same rate at all times, which is inconsistent with the varying slopes seen in the graph.

Would you like a detailed breakdown of why each option is incorrect or need help analyzing similar graphs?


Related Questions:

  1. How do you determine whether a function is increasing or decreasing using its graph?
  2. What does the slope of a graph tell us about the rate of change of a function?
  3. How can you identify when the rate of decrease is slowing down or speeding up in a function?
  4. What is the difference between a constant rate of change and a variable rate of change?
  5. How do you calculate the derivative of a function to analyze its behavior?

Tip: A steeper slope on a graph indicates a faster rate of change, while a flatter slope suggests a slower rate of change.

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Math Problem Analysis

Mathematical Concepts

Functions
Rate of Change
Graph Interpretation

Formulas

Slope = Δy / Δx (rate of change in a graph)

Theorems

Monotonic function properties

Suitable Grade Level

Grades 9-11