To determine which table shows exponential decay, we need to look for a consistent pattern where the y-values decrease exponentially as the x-values increase.
Let's analyze each table:
Table A:
x | y
-----
1 | 16
2 | 12
- The y-values (16, 12) are decreasing, but not in an exponential manner.
Table B:
x | y
-----
1 | 256
2 | 64
- The y-values (256, 64) are decreasing significantly. The pattern shows that each y-value is a function of a power of 4:
- 256 = 4^4
- 64 = 4^3 This indicates exponential decay.
Table C:
x | y
-----
1 | 16
2 | 4
- The y-values (16, 4) also show a decrease, but let's check if it's exponential:
- 16 = 4^2
- 4 = 4^1 This also indicates exponential decay.
Table D:
x | y
-----
3 | 20
4 | 25
5 | 16
- The y-values here (20, 25, 16) don't consistently decrease, so this does not represent exponential decay.
Conclusion:
Both Table B and Table C show exponential decay. However, since we are mainly looking for a clear exponential relationship:
- Table B shows a clear exponential decay from 256 to 64.
- Table C also shows a decreasing exponential relationship from 16 to 4.
Thus, the one that clearly exhibits exponential decay is Table B.