Sure, let's solve this step-by-step. In this problem, we are following a food chain and need to determine the energy transferred through each trophic level. It's known that energy transfer efficiency is roughly 10% between each trophic level.
Given that a bald eagle acquires [tex]\( 50 \)[/tex] kg of energy, we need to find out how much energy the zooplankton received from the phytoplankton.
1. Energy acquired by the bald eagle:
The bald eagle receives [tex]\( 50 \)[/tex] kg of energy.
2. Energy acquired by the sea ducks:
Since the energy transfer efficiency is 10%, the energy received by the sea ducks is:
[tex]\[
\text{Energy received by sea ducks} = \frac{\text{Energy received by bald eagle}}{0.1} = \frac{50}{0.1} = 500 \, \text{kg}
\][/tex]
3. Energy acquired by the bivalves:
Applying the same 10% efficiency, the energy received by the bivalves is:
[tex]\[
\text{Energy received by bivalves} = \frac{\text{Energy received by sea ducks}}{0.1} = \frac{500}{0.1} = 5000 \, \text{kg}
\][/tex]
4. Energy acquired by the zooplankton:
Again, with 10% efficiency, the energy received by the zooplankton is:
[tex]\[
\text{Energy received by zooplankton} = \frac{\text{Energy received by bivalves}}{0.1} = \frac{5000}{0.1} = 50000 \, \text{kg}
\][/tex]
Thus, the energy acquired by the zooplankton from the phytoplankton is [tex]\( 50000 \, \text{kg} \)[/tex].
So, the correct answer is:
[tex]\[ 50,000 \, \text{kg} \][/tex]
