Question

applied math
animals eat a lot! how much animal food does the sacramento zoo have to purchase and prepare? how many animals live at the park? use technology or ask a docent/keeper/employee to get estimates, and use those estimates to calculate how much money the zoo spends to feed its animals.

a. choose one animal to research how much it eats in a day. calculate how much food it would need in a year. draw or write about your findings.
b. choose one animal to research how much it eats. calculate how much food it would need in a year, and estimate how much that food will cost. then, multiply that figure by the number of that type of animal the park takes care of. record your calculations.
c. calculate estimates of food needs for each animal, each type of animal, and all of the animals at the park. do this per day and per year. estimate how much that would cost. record your calculations.

materials required: notebook, pen/pencil, calculator or smartphone (optional)
submission: your calculations, estimations, and conclusions, and any pictures/videos

teaching or learning notes:

Explanation:

Identify the project requirements

This is an open-ended applied mathematics project requiring research, estimation, and modeling. Since specific real-time data from the Sacramento Zoo is not provided in the prompt, we will use a representative, realistic model animal (the African Elephant) to demonstrate how to complete parts (a), (b), and (c).

Research and estimate for part a

Let's choose the African Elephant. An adult African elephant eats approximately \(150\text{ kg}\) (\(330\text{ lbs}\)) of food per day.
To find the yearly food requirement:

$$ 150\text{ kg/day} \times 365\text{ days/year} = 54,750\text{ kg/year} $$

Calculate cost and population for part b

Suppose the Sacramento Zoo cares for \(3\) African elephants.
Let's estimate the average cost of elephant feed (hay, vegetation, supplements) at \(1.50\text{ USD}\) per kilogram.
Yearly cost per elephant:

$$ 54,750\text{ kg} \times 1.50\text{ USD/kg} = 82,125\text{ USD/year} $$

Total yearly cost for all \(3\) elephants:

$$ 82,125\text{ USD/year} \times 3 = 246,375\text{ USD/year} $$

Scale to the entire zoo for part c

To estimate for the entire park, we categorize the zoo's population (approx. \(500\) animals) into three simplified feeding tiers:

1. Large Herbivores (e.g., elephants, giraffes): \(10\) animals, eating \(50\text{ kg/day}\) each at \(1.50\text{ USD/kg}\).
2. Medium Animals (e.g., big cats, primates): \(90\) animals, eating \(5\text{ kg/day}\) each at \(4.00\text{ USD/kg}\).
3. Small Animals (e.g., birds, reptiles): \(400\) animals, eating \(0.2\text{ kg/day}\) each at \(5.00\text{ USD/kg}\).

Let's calculate the total daily and yearly food mass and cost:

• Large:

$$ \text{Mass/day} = 10 \times 50 = 500\text{ kg} \implies 182,500\text{ kg/year} $$

$$ \text{Cost/day} = 500 \times 1.50 = 750\text{ USD} \implies 273,750\text{ USD/year} $$

• Medium:

$$ \text{Mass/day} = 90 \times 5 = 450\text{ kg} \implies 164,250\text{ kg/year} $$

$$ \text{Cost/day} = 450 \times 4.00 = 1,800\text{ USD} \implies 657,000\text{ USD/year} $$

• Small:

$$ \text{Mass/day} = 400 \times 0.2 = 80\text{ kg} \implies 29,200\text{ kg/year} $$

$$ \text{Cost/day} = 80 \times 5.00 = 400\text{ USD} \implies 146,000\text{ USD/year} $$

Sum the totals for the park

Total daily food mass:

$$ 500 + 450 + 80 = 1,030\text{ kg/day} $$

Total yearly food mass:

$$ 1,030 \times 365 = 375,950\text{ kg/year} $$

Total daily food cost:

$$ 750 + 1,800 + 400 = 2,950\text{ USD/day} $$

Total yearly food cost:

$$ 2,950 \times 365 = 1,076,750\text{ USD/year} $$

Answer:

Here is a complete, realistic model solution for your applied math project using representative estimations:

a. Single Animal Research (African Elephant)

• Daily Food Intake: Approximately \(150\text{ kg}\) (\(330\text{ lbs}\)) of hay, browse, and pellets.
• Yearly Food Calculation:

$$ 150\text{ kg/day} \times 365\text{ days/year} = 54,750\text{ kg/year} $$

b. Single Species Cost and Population

• Estimated Cost of Feed: \(1.50\text{ USD}\) per kg.
• Yearly Cost per Elephant:

$$ 54,750\text{ kg/year} \times 1.50\text{ USD/kg} = 82,125\text{ USD/year} $$

• Total Species Cost (for 3 Elephants):

$$ 82,125\text{ USD/year} \times 3 = 246,375\text{ USD/year} $$

c. Entire Zoo Estimation (approx. 500 animals)

• Daily Food Needs (All Animals): Approximately \(1,030\text{ kg/day}\)
• Yearly Food Needs (All Animals): Approximately \(375,950\text{ kg/year}\)
• Estimated Daily Cost: Approximately \(2,950\text{ USD/day}\)
• Estimated Yearly Cost: Approximately \(1,076,750\text{ USD/year}\)