Question
Which type of function best models the data in the table?
Type of Function
x y
1
10
2
100
3
1000
4
10000
(1 point)
Responses
quadratic
quadratic
cubic
cubic
exponential
exponential
linear
Type of Function
x y
1
10
2
100
3
1000
4
10000
(1 point)
Responses
quadratic
quadratic
cubic
cubic
exponential
exponential
linear
Answers
GPT-4o mini
To determine which type of function best models the data in the table you provided, we can analyze the relationship between the \(x\) and \(y\) values.
The table shows:
- When \(x = 1\), \(y = 10\)
- When \(x = 2\), \(y = 100\)
- When \(x = 3\), \(y = 1000\)
- When \(x = 4\), \(y = 10000\)
We can see that as \(x\) increases by 1, \(y\) increases by a factor of 10 (from 10 to 100 to 1000 to 10000). This rapid increase suggests that the relationship is not linear or quadratic, as those types would not cause such a multiplicative growth.
This pattern of growth indicates that an exponential function would best model this data. In general, an exponential function has the form \(y = a \cdot b^x\), where \(b\) is a constant factor of growth.
Therefore, the answer is:
**exponential**
The table shows:
- When \(x = 1\), \(y = 10\)
- When \(x = 2\), \(y = 100\)
- When \(x = 3\), \(y = 1000\)
- When \(x = 4\), \(y = 10000\)
We can see that as \(x\) increases by 1, \(y\) increases by a factor of 10 (from 10 to 100 to 1000 to 10000). This rapid increase suggests that the relationship is not linear or quadratic, as those types would not cause such a multiplicative growth.
This pattern of growth indicates that an exponential function would best model this data. In general, an exponential function has the form \(y = a \cdot b^x\), where \(b\) is a constant factor of growth.
Therefore, the answer is:
**exponential**