To determine the year [tex]\( y \)[/tex] in which the mercury levels in both bodies of water are the same, we need to set up an equation that equates the mercury levels for each respective body of water.
1. First Body of Water:
- Initial mercury level: [tex]\( 0.05 \, \text{ppb} \)[/tex]
- Rate of increase: [tex]\( 0.1 \, \text{ppb/year} \)[/tex]
- Mercury level after [tex]\( y \)[/tex] years: [tex]\( 0.05 + 0.1y \)[/tex]
2. Second Body of Water:
- Initial mercury level: [tex]\( 0.12 \, \text{ppb} \)[/tex]
- Rate of increase: [tex]\( 0.06 \, \text{ppb/year} \)[/tex]
- Mercury level after [tex]\( y \)[/tex] years: [tex]\( 0.12 + 0.06y \)[/tex]
Next, we set the equations for the mercury levels equal to each other because we want to find when they are the same:
[tex]\[ 0.05 + 0.1 y = 0.12 + 0.06 y \][/tex]
This equation expresses that the mercury level in the first body of water after [tex]\( y \)[/tex] years (left side) is equal to the mercury level in the second body of water after [tex]\( y \)[/tex] years (right side).
Therefore, the correct equation that can be used to find [tex]\( y \)[/tex] is:
[tex]\[ 0.05 + 0.1 y = 0.12 + 0.06 y \][/tex]
Answer:
[tex]\[ 0.05 + 0.1 y = 0.12 + 0.06 y \][/tex]
