Question

Which type of function best models the data in the table?

Time and Distance Data

Time (sec) Distance (miles)
1
3

2
9

3
27

4
81

5
243

(1 point)
Responses

exponential
exponential

cubic
cubic

linear
linear

quadratic

Answer 1

To determine which type of function best models the given data, we can analyze the pattern of the distance values corresponding to the time values:

- When time is 1 sec, distance is 3 miles.
- When time is 2 sec, distance is 9 miles.
- When time is 3 sec, distance is 27 miles.
- When time is 4 sec, distance is 81 miles.
- When time is 5 sec, distance is 243 miles.

Observing the distances, we notice that:

- \(3 = 3^1\)
- \(9 = 3^2\)
- \(27 = 3^3\)
- \(81 = 3^4\)
- \(243 = 3^5\)

The distances can be represented as \(D = 3^t\) where \(D\) is the distance and \(t\) is the time in seconds.

Since the distances grow exponentially with time, the function that best models the data is **exponential**.

So, the answer is:

**exponential**