Question

Ericka observed the total variation in the water level over 6.2 years to be −13.64 mm. She compared this to the average annual trend, which shows the water level rising 1.8 mm/year. Remember, she used 6.2 years as her time period. What is the difference between how much average water levels rose and how much the water level fell in the part of the river she observed?

millimeters

Answer 1

To find the difference between how much the average water levels rose and how much the water level fell in the part of the river Ericka observed, we can follow these steps:

1. **Calculate the total increase in water level over 6.2 years:**
The average annual trend is 1.8 mm/year. Over 6.2 years, the total increase would be:
\[
\text{Total increase} = 1.8 \, \text{mm/year} \times 6.2 \, \text{years} = 11.16 \, \text{mm}
\]

2. **Note the total decrease in water level over the same period:**
The observed total variation (or decrease) in the water level is given as -13.64 mm. The negative sign indicates a decrease.

3. **Calculate the difference between the increase and the decrease:**
We want to find the difference between the total increase and the total decrease:
\[
\text{Difference} = \text{Total increase} - \text{Total decrease}
\]
Substituting the values we have:
\[
\text{Difference} = 11.16 \, \text{mm} - (-13.64 \, \text{mm}) = 11.16 \, \text{mm} + 13.64 \, \text{mm} = 24.8 \, \text{mm}
\]

Thus, the difference between how much average water levels rose and how much the water level fell is:

\[
\boxed{24.8 \, \text{mm}}
\]