Question

Which table shows exponential decay?

Answer options with 4 options
A.
x y
1 16
2 12
3 8
4 4
5 0

C.
x y
1 256
2 64
3 16
4 4
5 1

B.
x y
1 64
2 49
3 36
4 25
5 16

D.
x y
1 840
2 120
3 20
4 4
5 1

Answer 1

To determine which table shows exponential decay, we need to look for a consistent pattern where the values decrease rapidly in a multiplicative way (usually by a consistent percentage or factor).

Let's evaluate each table:

**A.**
```
x y
1 16
2 12
3 8
4 4
5 0
```
- The values are decreasing but not at a consistent exponential rate, as they're not being multiplied by a consistent factor.

**B.**
```
x y
1 64
2 49
3 36
4 25
5 16
```
- This represents a polynomial decay, as the differences between the numbers decrease progressively.

**C.**
```
x y
1 256
2 64
3 16
4 4
5 1
```
- Here, the values are decreasing in a consistent multiplicative way (dividing by 4 each step: 256/4 = 64, 64/4 = 16, 16/4 = 4, 4/4 = 1). This is indicative of exponential decay.

**D.**
```
x y
1 840
2 120
3 20
4 4
5 1
```
- The values again do not decrease at a consistent multiplicative rate.

Based on this analysis, the table that shows exponential decay is:

**C.**
```
x y
1 256
2 64
3 16
4 4
5 1
```