Question

Earth Science The table shows the year-to-year changes in the mean January water level of Lake Superior during the period 1997–2001. Positive changes represent increases in the water level, while negative changes represent decreases. In 2001, the water level was 182.98 meters. What was the water level in 1997?

1 Find the overall change in the water level from 1997 to 2001 by adding the changes in the table.

2 Write an equation that you can use to find the water level in 1997.

3 Solve your equation. What was Lake Superior’s water level in 1997?

Short answer

1. Overall change in water level from $1997$to $2001$ $=-0.61$.

2.Equation to find water level in $1997$is $182.98=x-0.61$.

3. Water level in $1997$is $183.59$meters.

Step-by-step solution

a.Step-1- Writing formula from given information

Overall change in water level $=$ change in $1997$to $1998$ + change in $1998$to $1999$+ change in $1999$ to$2000$+ change in $2000$to $2001$.

Step-2- Substituting values from given information

On substituting values, we get,

Overall change in water level $=-0.19-0.28+0.04-0.18$.

$\Rightarrow$ Overall change in water level $=-0.61$

Step-3- Conclusion

Therefore,

Overall change in water level from $1997$to $2001$ $=-0.61$

b.Step-1- Writing formula from given information

Let us assume Water level in $1997$be $x$.

From given information, we came to know that,

Water level in $2001$= water level in $1997$+ change in water level from $1997$to $2001$.

Step-2-Substituting values from given information

On substituting values, we get

$\Rightarrow$ $182.98=x-0.61$.

Step-3-Conclusion

Therefore, the equation to find water level in $1997$is $182.98=x-0.61$.

c.Step-1- Taking above part equation

From part -b, we came to know that the equation to find water level in $1997$is $182.98=x-0.61$.

Step-2-Solve for value of x

On solving it, we get,

$182.98=x-0.61$.

Adding $0.61$on both sides We get

$\begin{array}{l}182.98+0.61=x-0.61+0.61\\ x=182.98+0.61\\ x=183.59\end{array}$

Step-3-Conclusion

Therefore, the water level in $1997$is $183.59$meters.