Question

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


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

Answer 1

To determine the type of growth represented by the values in the table, we can analyze the values given and look for a pattern.

The values are:
- 1 corresponds to 14
- 2 corresponds to 56
- 3 corresponds to 224
- 4 corresponds to 896
- 5 corresponds to 3584

We can look at the ratios of consecutive values to check for exponential growth:

- \( \frac{56}{14} = 4 \)
- \( \frac{224}{56} = 4 \)
- \( \frac{896}{224} = 4 \)
- \( \frac{3584}{896} = 4 \)

Since the ratio between each pair of consecutive terms is consistently 4, this suggests that the function represents exponential growth, as each subsequent value is obtained by multiplying the previous value by 4.

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