Question

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

X Y
1 972
2 324
3 108
4 36
5 12

Linear growth
Linear decay
Exponential decay
Exponential growth

Answer 1

To determine the type of function represented by the values in the table, let's examine the data:

X | Y
--|---
1 | 972
2 | 324
3 | 108
4 | 36
5 | 12

First, we should observe the changes in Y as X increases:

1. From 1 to 2: 972 to 324 (decrease by a factor of approximately 3)
2. From 2 to 3: 324 to 108 (decrease by a factor of 3)
3. From 3 to 4: 108 to 36 (decrease by a factor of 3)
4. From 4 to 5: 36 to 12 (decrease by a factor of 3)

Y is decreasing by a constant factor (about 3) as X increases. This suggests a pattern consistent with exponential decay, where the Y values are decreasing by a consistent ratio.

Thus, the description that matches the function represented by the values in the table is **Exponential decay**.