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





linear
linear

cubic
cubic

quadratic
quadratic

exponential

Answer 1

To determine which type of function best models the data from the table, we can analyze the relationship between the \( x \) and \( y \) values.

Looking at the data:

- For \( x = 1 \), \( y = 10 \)
- For \( x = 2 \), \( y = 100 \)
- For \( x = 3 \), \( y = 1000 \)
- For \( x = 4 \), \( y = 10000 \)

We can observe how the \( y \) values change as \( x \) increases.

- From \( x = 1 \) to \( x = 2 \), \( y \) increases by a factor of 10 (from 10 to 100).
- From \( x = 2 \) to \( x = 3 \), \( y \) increases by a factor of 10 (from 100 to 1000).
- From \( x = 3 \) to \( x = 4 \), \( y \) increases by a factor of 10 (from 1000 to 10000).

The consistent multiplicative factor of 10 indicates that the relationship is not linear, quadratic, or cubic.

Instead, this pattern suggests that the function is **exponential**. In an exponential function, \( y \) can be expressed in the form \( y = a \cdot b^x \), where \( b \) is a constant greater than 1 (in this case, it appears to be 10).

Thus, the best type of function to model the given data is **exponential**.