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

1 answer

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