3. If a hawk eats 30% of the weasel population, weasels eat 30% of the mouse population, and
mice eat 20% of the wheat plants, calculate the total numbers of each organism that exist in
this ecosystem
a. Start by finding how many weasels there are to support the one hawk
i. # of weasels eaten 7.3 = total weasels
ii. total weasels x # of mice needed / .3 = total mice
iii. total mice x # of wheat plants needed / .2 = total wheat plants

a. Approximately 1,003 weasels, 3,345 mice and 16,729 wheat plants per one hawk are in the ecosystem

Explanation:

The percentage of the weasel population eaten by a hawk = 30%

The percentage of the mouse population eaten by a weasel = 30%

The percentage of the wheat plants population eaten by a mice = 20%

a. One hawk needs 330 kJ of energy per day, which gives 330 kJ × 365 = 120,450 kJ per year

Let 'x' represent the number of weasels to support one hawk, we have;

0.3 × x = 120,450 kJ/year/(400 kJ) = 301.125

x = 301.125/0.3 = 1,003.75

The number of weasels required to support one hawk per year ≈ 1,003 weasels

The total weasels ≈ 1,003

ii) The number of mice needed, y = x/0.3 = 1,003.75/0.3 = 3,345.8

The total mice, y ≈ 3,345 mice

iii) The number of wheat flower needed, z = y/0.2

∴ The number of wheat flower needed, z = 3,345.8/0.2 ≈ 16,729.1

The total wheat plants ≈ 16,729.