Question

1. match the distance increase with the correct decrease in

distance increase | decrease in intensity
×2 | 1/4
×4 |
×5 |
×8 |
×10 |

x5

x8

x10

x4

choices
1/16
1/64
1/100
1/25

Explanation:

Step1: Analyze the pattern for ×2

When distance increases by ×2, intensity decreases by \( \frac{1}{4}=\frac{1}{2^2} \). So the pattern is: if distance increases by \( \times n \), intensity decreases by \( \frac{1}{n^2} \).

Step2: Calculate for ×4

For \( n = 4 \), intensity decrease is \( \frac{1}{4^2}=\frac{1}{16} \).

Step3: Calculate for ×5

For \( n = 5 \), intensity decrease is \( \frac{1}{5^2}=\frac{1}{25} \).

Step4: Calculate for ×8

For \( n = 8 \), intensity decrease is \( \frac{1}{8^2}=\frac{1}{64} \).

Step5: Calculate for ×10

For \( n = 10 \), intensity decrease is \( \frac{1}{10^2}=\frac{1}{100} \).

Answer:

• ×4: \( \frac{1}{16} \)
• ×5: \( \frac{1}{25} \)
• ×8: \( \frac{1}{64} \)
• ×10: \( \frac{1}{100} \)