To determine how many years it might have taken to accumulate the slip that resulted in the observed offset of the stream, follow these steps:
1. Identify the given data:
- Slip rate: The slip rate is 6 cm per year.
- Stream offset: We have two values mentioned here, -303 meters and -160 meters. However, we will first focus on the -303 meters offset.
2. Convert the stream offset to centimeters:
- Since 1 meter equals 100 centimeters, an offset of -303 meters can be converted by:
[tex]\[
\text{Stream offset in cm} = -303 \times 100 = -30300 \text{ cm}
\][/tex]
- We consider the absolute value because the negative sign simply denotes direction:
[tex]\[
\text{Stream offset in cm} = 30300 \text{ cm}
\][/tex]
3. Calculate the number of years taken to accumulate the slip:
- Using the formula \( \text{Time} = \frac{\text{Offset}}{\text{Slip rate}} \):
[tex]\[
\text{Time} = \frac{30300 \text{ cm}}{6 \text{ cm/year}}
\][/tex]
[tex]\[
\text{Time} = 5050 \text{ years}
\][/tex]
4. Match the calculated time with the given options:
- The options provided are:
a. 2667 years
b. 5033 years
c. 1010 years
d. 10100 years
- Our calculated time of 5050 years is closest to option b (5033 years).
Therefore, the time it might have taken to accumulate the slip that resulted in the observed offset of the stream at -303 meters is closest to:
b. ~5033 years
