Question

Which description matches the function represented by the values in this table?
x

1
14
2
56
3
224
4
896
5
3584
linear decay linear growth
exponential decay exponential growth

Answer 1

To determine the type of function represented by the values in the table, let's analyze the values for \( x \) and the corresponding outputs:

| \( x \) | Output |
|---------|--------|
| 1 | 14 |
| 2 | 56 |
| 3 | 224 |
| 4 | 896 |
| 5 | 3584 |

First, let's look at the ratios of consecutive outputs to see if they indicate exponential growth:

- From \( x = 1 \) to \( x = 2 \): \( \frac{56}{14} = 4 \)
- From \( x = 2 \) to \( x = 3 \): \( \frac{224}{56} = 4 \)
- From \( x = 3 \) to \( x = 4 \): \( \frac{896}{224} = 4 \)
- From \( x = 4 \) to \( x = 5 \): \( \frac{3584}{896} = 4 \)

Since the ratio of consecutive outputs is constant (4), this indicates that the function is an exponential growth function.

Therefore, the correct description that matches the function represented by the values in this table is **exponential growth**.