Manuel is also in Mr. Whittaker’s science class. He observed that the water level rose 1.8 millimeters per year, which matches the average annual trend. This occurred for 2.2 years. Explain how to determine the total variation in water level. How can you check your answer?

Answer 1

To determine the total variation in water level based on the given information, you can follow these steps:

1. Identify the Variables:

   • Annual rise in water level: 1.8 millimeters per year
   • Duration of observation: 2.2 years

2. Calculate the Total Variation: To find the total variation in the water level over the 2.2 years, you can use the formula: \[ \text{Total Variation} = \text{Rise per Year} \times \text{Number of Years} \] Plugging in the values: \[ \text{Total Variation} = 1.8 , \text{mm/year} \times 2.2 , \text{years} \] Carry out the multiplication: \[ \text{Total Variation} = 1.8 \times 2.2 = 3.96 , \text{mm} \]

3. Check Your Answer: To verify the calculation, you can break it down into smaller steps or use an alternative method:

   • Break down the multiplication:

     • Calculate \(1.8 \times 2\): \[ 1.8 \times 2 = 3.6 , \text{mm} \]
     • Calculate \(1.8 \times 0.2\): \[ 1.8 \times 0.2 = 0.36 , \text{mm} \]
     • Add these results together: \[ 3.6 , \text{mm} + 0.36 , \text{mm} = 3.96 , \text{mm} \]

   • Alternatively, use a calculator for \(1.8 \times 2.2\) to confirm it gives \(3.96\) mm.

By following these steps, you’ll have calculated the total variation in water level as \(3.96\) millimeters over the period of 2.2 years, and the verification steps will confirm that your calculations are accurate.