Science:Math Exam Resources/Courses/MATH102/December 2019/Question 04 (d)

MATH102 December 2019

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Question 04 (d)

Remember our fishy friends? The quality of hatching of larvae of cold-water fish depends on the temperature of the water. Each hatch is given a quality ranking from 0 to 10, with 10 being a perfect hatch.

Based on the temperature, we can predict how much energy a fish invests in finding enough food to produce healthy eggs, ${\displaystyle E_{\mathrm {eggs} }}$. Fish also need to spend some energy in being alert for predators that want to eat them, ${\displaystyle E_{\mathrm {alert} }}$.

The fish try to minimize the total amount of energy used, ${\displaystyle E_{\text{eggs}}+E_{\text{alert}}}$, by seeking out areas of optimal temperature.

Using the graph above, choose the one statement below that best describes the situation.

1. At lower temperatures, there are more predators, so the fish try to seek out waters that are warmer than ${\displaystyle 4^{\circ }}$, but still cold enough to lay eggs in.
2. The total amount of energy expended is optimal at around ${\displaystyle 7^{\circ }}$, so the fish seek out waters with this temperature to find the most food to gain energy to lay their eggs.
3. The warmer the water, the better for the eggs, because at high temperatures, the total amount of energy does not change much as temperature changes.
4. Since there always will be predators around, the fish should focus on foraging to produce eggs, and stay in waters with the optimal temperature ${\displaystyle 3^{\circ }}$.
5. The total amount of energy invested is minimal in waters with temperatures of around ${\displaystyle 2^{\circ }}$, although this temperature does not have the most abundant food.
6. The energy spent towards being alert is highest at ${\displaystyle 5^{\circ }}$ while the energy for producing eggs is lowest around ${\displaystyle 3^{\circ }}$, so fish should thrive best in waters of around ${\displaystyle 4^{\circ }}$.
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