Biology worksheet challenging students to calculate the energy efficiency of a female lion hunting various prey species.

Problem Overview:

The task involves determining the maximum number of each prey species a female lion can hunt using her stored energy (15,000 kcal) while ensuring she gains enough energy to survive (at least 13,500 kcal per day). We need to calculate the net energy gained for each prey species and decide if hunting them alone is worthwhile.

Given Data:

1. Stored Energy: 15,000 kcal
2. Daily Energy Requirement: 13,500 kcal
3. Prey Species Data:
- Meerkat: Mass = 0.77 kg, Energy cost = -3,000 kcal, Energy gain = +5,000 kcal
- Warthog: Mass = 60 kg, Energy cost = -5,000 kcal, Energy gain = +12,000 kcal
- Wildebeest: Mass = 265 kg, Energy cost = -10,000 kcal, Energy gain = +25,000 kcal
- Zebra: Mass = 310 kg, Energy cost = -55,000 kcal, Energy gain = +170,000 kcal

Steps to Solve:

1. Calculate the Net Energy Gained per Prey:
\[
\text{Net Energy Gained} = \text{Energy Gain} - \text{Energy Cost}
\]

2. Determine the Maximum Number of Each Prey She Can Hunt:
\[
\text{Maximum Number of Prey} = \left\lfloor \frac{\text{Stored Energy}}{\text{Energy Cost per Prey}} \right\rfloor
\]
Ensure that the total energy cost does not exceed 15,000 kcal.

3. Check if Hunting Each Prey is Worthwhile:
- The net energy gained must be positive.
- The total energy gained must cover the daily requirement of 13,500 kcal.

Calculations:

#### Meerkat
- Energy Cost: -3,000 kcal
- Energy Gain: +5,000 kcal
- Net Energy Gained per Meerkat:
\[
\text{Net Energy Gained} = 5,000 - 3,000 = 2,000 \text{ kcal}
\]
- Maximum Number of Meerkats:
\[
\text{Maximum Number} = \left\lfloor \frac{15,000}{3,000} \right\rfloor = 5
\]
- Total Energy Cost for 5 Meerkats:
\[
\text{Total Cost} = 5 \times 3,000 = 15,000 \text{ kcal}
\]
- Total Energy Gained for 5 Meerkats:
\[
\text{Total Gain} = 5 \times 5,000 = 25,000 \text{ kcal}
\]
- Net Energy Gained for 5 Meerkats:
\[
\text{Net Gain} = 25,000 - 15,000 = 10,000 \text{ kcal}
\]
- Is it Worthwhile?:
No, because the net energy gained (10,000 kcal) is less than the daily requirement (13,500 kcal).

#### Warthog
- Energy Cost: -5,000 kcal
- Energy Gain: +12,000 kcal
- Net Energy Gained per Warthog:
\[
\text{Net Energy Gained} = 12,000 - 5,000 = 7,000 \text{ kcal}
\]
- Maximum Number of Warthogs:
\[
\text{Maximum Number} = \left\lfloor \frac{15,000}{5,000} \right\rfloor = 3
\]
- Total Energy Cost for 3 Warthogs:
\[
\text{Total Cost} = 3 \times 5,000 = 15,000 \text{ kcal}
\]
- Total Energy Gained for 3 Warthogs:
\[
\text{Total Gain} = 3 \times 12,000 = 36,000 \text{ kcal}
\]
- Net Energy Gained for 3 Warthogs:
\[
\text{Net Gain} = 36,000 - 15,000 = 21,000 \text{ kcal}
\]
- Is it Worthwhile?:
Yes, because the net energy gained (21,000 kcal) is greater than the daily requirement (13,500 kcal).

#### Wildebeest
- Energy Cost: -10,000 kcal
- Energy Gain: +25,000 kcal
- Net Energy Gained per Wildebeest:
\[
\text{Net Energy Gained} = 25,000 - 10,000 = 15,000 \text{ kcal}
\]
- Maximum Number of Wildebeests:
\[
\text{Maximum Number} = \left\lfloor \frac{15,000}{10,000} \right\rfloor = 1
\]
- Total Energy Cost for 1 Wildebeest:
\[
\text{Total Cost} = 1 \times 10,000 = 10,000 \text{ kcal}
\]
- Total Energy Gained for 1 Wildebeest:
\[
\text{Total Gain} = 1 \times 25,000 = 25,000 \text{ kcal}
\]
- Net Energy Gained for 1 Wildebeest:
\[
\text{Net Gain} = 25,000 - 10,000 = 15,000 \text{ kcal}
\]
- Is it Worthwhile?:
Yes, because the net energy gained (15,000 kcal) is greater than the daily requirement (13,500 kcal).

#### Zebra
- Energy Cost: -55,000 kcal
- Energy Gain: +170,000 kcal
- Net Energy Gained per Zebra:
\[
\text{Net Energy Gained} = 170,000 - 55,000 = 115,000 \text{ kcal}
\]
- Maximum Number of Zebras:
\[
\text{Maximum Number} = \left\lfloor \frac{15,000}{55,000} \right\rfloor = 0
\]
- Total Energy Cost for 0 Zebras:
\[
\text{Total Cost} = 0 \times 55,000 = 0 \text{ kcal}
\]
- Total Energy Gained for 0 Zebras:
\[
\text{Total Gain} = 0 \times 170,000 = 0 \text{ kcal}
\]
- Net Energy Gained for 0 Zebras:
\[
\text{Net Gain} = 0 - 0 = 0 \text{ kcal}
\]
- Is it Worthwhile?:
No, because the maximum number of zebras she can hunt is 0.

Final Table:

| Species | Number of Prey Hunted and Consumed | Energy Cost per Prey (-kcal) | Total Energy Cost for Total Number of Prey (-kcal) | Energy Available per Prey (+kcal) | Total Energy Available for Total Number of Prey (+kcal) | Net Energy Gained (+kcal) | Is this Species Worthwhile to Hunt Alone? (Yes/No) |
|---------------|------------------------------------|------------------------------|--------------------------------------------------|-----------------------------------|-------------------------------------------------------|---------------------------|-----------------------------------------------------|
| Meerkat | 5 | 3,000 | 15,000 | 5,000 | 25,000 | 10,000 | No |
| Warthog | 3 | 5,000 | 15,000 | 12,000 | 36,000 | 21,000 | Yes |
| Wildebeest | 1 | 10,000 | 10,000 | 25,000 | 25,000 | 15,000 | Yes |
| Zebra | 0 | 55,000 | 0 | 170,000 | 0 | 0 | No |

Final Answer:

\[
\boxed{
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
\text{Species} & \text{Number of Prey Hunted and Consumed} & \text{Energy Cost per Prey (-kcal)} & \text{Total Energy Cost for Total Number of Prey (-kcal)} & \text{Energy Available per Prey (+kcal)} & \text{Total Energy Available for Total Number of Prey (+kcal)} & \text{Net Energy Gained (+kcal)} & \text{Is this Species Worthwhile to Hunt Alone? (Yes/No)} \\
\hline
\text{Meerkat} & 5 & 3,000 & 15,000 & 5,000 & 25,000 & 10,000 & \text{No} \\
\hline
\text{Warthog} & 3 & 5,000 & 15,000 & 12,000 & 36,000 & 21,000 & \text{Yes} \\
\hline
\text{Wildebeest} & 1 & 10,000 & 10,000 & 25,000 & 25,000 & 15,000 & \text{Yes} \\
\hline
\text{Zebra} & 0 & 55,000 & 0 & 170,000 & 0 & 0 & \text{No} \\
\hline
\end{array}
}
\]