Question

Which type of function best models the data in the table?
(x,y) (1,10) (2,100) (3,1000) (4,10000)


(1 point)
Responses

linear
linear

quadratic
quadratic

cubic
cubic

exponential

Answer 1

To determine which type of function best models the given data points \((1, 10)\), \((2, 100)\), \((3, 1000)\), and \((4, 10000)\), let's analyze the pattern in the y-values:

- When \(x = 1\), \(y = 10\)
- When \(x = 2\), \(y = 100\) (which is \(10 \cdot 10\))
- When \(x = 3\), \(y = 1000\) (which is \(10 \cdot 100\))
- When \(x = 4\), \(y = 10000\) (which is \(10 \cdot 1000\))

From this, we can see that each time \(x\) increases by 1, \(y\) is multiplied by 10. This indicates an exponential growth pattern. Specifically, we can express the output \(y\) in terms of \(x\) as follows:

\[
y = 10 \cdot 10^{(x-1)} = 10^x
\]

Thus, the best function to model the data is an **exponential** function.

Therefore, the correct response is:

**exponential**