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

quadratic
quadratic

exponential
exponential

linear
linear

cubic

Answer 1

To determine which type of function best models the given data, let's analyze the relationship between time (in seconds) and distance (in miles).

The table presents the following values:

- At 1 sec: 3 miles
- At 2 sec: 9 miles
- At 3 sec: 27 miles
- At 4 sec: 81 miles
- At 5 sec: 243 miles

Looking at the distance values, we can note that:

- Each distance value appears to be increasing rapidly as time increases.
- Specifically, each distance value can be expressed as \(3^n\):
- \(3^1 = 3\)
- \(3^2 = 9\)
- \(3^3 = 27\)
- \(3^4 = 81\)
- \(3^5 = 243\)

This suggests an exponential growth pattern in the distance based on time.

Therefore, the best function that fits this data is an **exponential** function.

So the answer is **exponential**.