Which table represents an exponential function?
| x | y |
|---|---|
| 1 | 5 |
| 2 | 10 |
| 3 | 15 |
| 4 | 20 |
| 5 | 25 |
Answer (2)
Calculate the ratios between consecutive y values: 5 10 = 2 , 10 15 = 1.5 , 15 20 = 3 4 , 20 25 = 4 5 .
Since the ratios are not constant, the table does not represent an exponential function.
The function is linear.
The table does not represent an exponential function: F a l se .
Explanation
Analyzing the Problem We are given a table of x and y values and asked to determine if it represents an exponential function. To do this, we need to check if the ratio between consecutive y values is constant. If it is, then the table represents a geometric sequence, which could be an exponential function. If the ratios are not equal, then the table does not represent an exponential function.
Calculating Ratios Let's calculate the ratios between consecutive y values:
Ratio 1: 5 10 = 2
Ratio 2: 10 15 = 1.5
Ratio 3: 15 20 = 3 4 ≈ 1.33
Ratio 4: 20 25 = 4 5 = 1.25
Determining if the Function is Exponential Since the ratios between consecutive y values are not constant (2, 1.5, 1.33, 1.25), the table does not represent an exponential function.
Conclusion The ratios are not constant, so the function is not exponential. The y values increase by 5 for each increase of 1 in x . This indicates a linear relationship.
Examples
Exponential functions are used to model population growth, radioactive decay, and compound interest. For example, if a population of bacteria doubles every hour, the population can be modeled by an exponential function. Similarly, the amount of a radioactive substance decreases exponentially over time.
The table does not represent an exponential function because the ratios between consecutive y values are not constant. Instead, it indicates a linear relationship where y increases by 5 for each increase in x . Therefore, the answer is that this table does not represent an exponential function.
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