Question

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

X Y
1 14
2 56
3 224
4 896
5 3584
Linear growth
Linear decay
Exponential decay
Exponential growth

Answer 1

To determine the type of function represented by the values in the table, we should first analyze the relationship between the values of \( X \) and \( Y \).

The values provided are:

- \( X = 1, Y = 14 \)
- \( X = 2, Y = 56 \)
- \( X = 3, Y = 224 \)
- \( X = 4, Y = 896 \)
- \( X = 5, Y = 3584 \)

Let's look at how \( Y \) changes as \( X \) increases.

1. Calculate the ratio of successive \( Y \) values:
- From \( Y(1) \) to \( Y(2) \): \( \frac{56}{14} = 4 \)
- From \( Y(2) \) to \( Y(3) \): \( \frac{224}{56} = 4 \)
- From \( Y(3) \) to \( Y(4) \): \( \frac{896}{224} = 4 \)
- From \( Y(4) \) to \( Y(5) \): \( \frac{3584}{896} = 4 \)

The ratio of each successive \( Y \) value is constant (4). This indicates that \( Y \) is growing by a factor of 4 for every increase of 1 in \( X \).

Since the \( Y \) values are increasing by a constant multiplicative factor, this is indicative of exponential growth.

Thus, the correct description that matches the function is **Exponential growth**.