Question

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

Answer 1

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**.