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Which set of ordered pairs could be generated by an exponential function?

Question

Which set of ordered pairs could be generated by an exponential function?

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Solution

Step 1: Define the Problem

Identify which set of ordered pairs can be represented by an exponential function. An exponential function has the form y=abx y = a \cdot b^x , where a0 a \neq 0 , b>0 b > 0 , and b1 b \neq 1 .

Step 2: Break Down the Problem

  1. Understand the characteristics of exponential functions.
  2. Analyze each set of ordered pairs to see if they fit the form of an exponential function.

Step 3: Apply Relevant Concepts

  • Exponential functions have a constant ratio between consecutive y y -values when the x x -values increase by a constant amount.
  • Check if the ratio y2y1=y3y2= \frac{y_2}{y_1} = \frac{y_3}{y_2} = \ldots holds for each set of ordered pairs.

Step 4: Analysis, Verify and Summarize

  1. For each set of ordered pairs, calculate the ratio of consecutive y y -values.
  2. Verify if the ratio is constant across the pairs.

Final Answer

The set of ordered pairs that maintains a constant ratio between consecutive y y -values corresponds to an exponential function.

This problem has been solved

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