To determine how much water can be pumped from the aquifer, we need to ensure that the water budget is balanced. This implies that the total amount of water entering the aquifer should be equal to the total amount of water leaving the aquifer.
1. Water Inflow: The aquifer receives [tex]\(20 \, \text{m}^3\)[/tex] of precipitation.
2. Natural Losses: The aquifer loses [tex]\(2 \, \text{m}^3\)[/tex] of water through natural movement.
We need to find the amount of water that can be pumped, which we'll call [tex]\( \text{water\_pumped} \)[/tex]. For the water budget to be balanced, the inflow should equal the outflow:
[tex]\[
\text{Total Inflow} = \text{Total Outflow}
\][/tex]
Total Inflow:
The total inflow is simply the precipitation:
[tex]\[
\text{Total Inflow} = 20 \, \text{m}^3
\][/tex]
Total Outflow:
The total outflow consists of the natural losses plus the water pumped:
[tex]\[
\text{Total Outflow} = \text{Natural Losses} + \text{Water\_Pumped}
\][/tex]
Given the data:
[tex]\[
\text{Natural Losses} = 2 \, \text{m}^3
\][/tex]
To balance the equation:
[tex]\[
20 \, \text{m}^3 = 2 \, \text{m}^3 + \text{Water\_Pumped}
\][/tex]
Solving for [tex]\( \text{Water\_Pumped} \)[/tex]:
[tex]\[
\text{Water\_Pumped} = 20 \, \text{m}^3 - 2 \, \text{m}^3
\][/tex]
[tex]\[
\text{Water\_Pumped} = 18 \, \text{m}^3
\][/tex]
So, the amount of water that can be pumped from the aquifer while maintaining a balanced water budget is [tex]\(18 \, \text{m}^3\)[/tex].
[tex]\[
\boxed{18 \, \text{m}^3}
\][/tex]
