Which table shows exponential decay?

xy

1 16

2 12

A.

38

44

50

xy

1 256

2 64

c.

16

4

51

164

1840

249

2 120

B. 336

D.

3 20

4 25

44

5 16

51

1 answer

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.