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
linear
linear
cubic
cubic
exponential
Type of Function
x y
1
10
2
100
3
1000
4
10000
(1 point)
Responses
quadratic
quadratic
linear
linear
cubic
cubic
exponential
Answers
GPT-4o mini
To determine the best type of function that models the data in the table, let's analyze the values of \( y \) corresponding to each value of \( x \):
- When \( x = 1, y = 10^1 = 10 \)
- When \( x = 2, y = 10^2 = 100 \)
- When \( x = 3, y = 10^3 = 1000 \)
- When \( x = 4, y = 10^4 = 10000 \)
From the pattern in the data, we see that \( y \) is equal to \( 10 \) raised to the power of \( x \). The relationship indicates that as \( x \) increases by 1, \( y \) increases by a factor of 10, which is characteristic of an exponential function.
Thus, the best type of function that models the data is **exponential**.
- When \( x = 1, y = 10^1 = 10 \)
- When \( x = 2, y = 10^2 = 100 \)
- When \( x = 3, y = 10^3 = 1000 \)
- When \( x = 4, y = 10^4 = 10000 \)
From the pattern in the data, we see that \( y \) is equal to \( 10 \) raised to the power of \( x \). The relationship indicates that as \( x \) increases by 1, \( y \) increases by a factor of 10, which is characteristic of an exponential function.
Thus, the best type of function that models the data is **exponential**.