Question
What kind of relationship is shown in the table?
2019 1542
2020 1604
2021 1668
2022 1735
Quadratic
Logarithmic
Linear
Exponential
2019 1542
2020 1604
2021 1668
2022 1735
Quadratic
Logarithmic
Linear
Exponential
Answers
GPT-4o mini
To determine the type of relationship shown in the table, we can analyze the data points for any patterns.
- **Linear relationships** can be identified by a constant difference between consecutive values.
- **Exponential relationships** tend to show a consistent percentage increase (the ratio of consecutive terms is constant).
- **Quadratic relationships** typically show a consistent second difference (the differences of the differences).
- **Logarithmic relationships** grow quickly at first and then level off.
Let's examine the data:
- 2019 to 2020: 1604 - 1542 = 62
- 2020 to 2021: 1668 - 1604 = 64
- 2021 to 2022: 1735 - 1668 = 67
The difference between the consecutive years is increasing (62, 64, 67), which suggests that it's not linear, as linear would be a constant difference.
### Checking for Exponential Growth:
Let's calculate the ratios between consecutive years:
- 2020/2019: 1604 / 1542 ≈ 1.04
- 2021/2020: 1668 / 1604 ≈ 1.04
- 2022/2021: 1735 / 1668 ≈ 1.04
The ratios are approximately constant, indicating an exponential growth pattern.
Therefore, the relationship shown in the table is **Exponential**.
- **Linear relationships** can be identified by a constant difference between consecutive values.
- **Exponential relationships** tend to show a consistent percentage increase (the ratio of consecutive terms is constant).
- **Quadratic relationships** typically show a consistent second difference (the differences of the differences).
- **Logarithmic relationships** grow quickly at first and then level off.
Let's examine the data:
- 2019 to 2020: 1604 - 1542 = 62
- 2020 to 2021: 1668 - 1604 = 64
- 2021 to 2022: 1735 - 1668 = 67
The difference between the consecutive years is increasing (62, 64, 67), which suggests that it's not linear, as linear would be a constant difference.
### Checking for Exponential Growth:
Let's calculate the ratios between consecutive years:
- 2020/2019: 1604 / 1542 ≈ 1.04
- 2021/2020: 1668 / 1604 ≈ 1.04
- 2022/2021: 1735 / 1668 ≈ 1.04
The ratios are approximately constant, indicating an exponential growth pattern.
Therefore, the relationship shown in the table is **Exponential**.