We wondered, based on the rate at which the population is increasing, how long it would take for the amount of food needed to support the population to exceed the amount of food produced. We explored different variables to see how each of them would affect the results.

**Step 1: Calorie Intake**

In order to determine the population limit, we first had to do some basic calculations.

- Current total population: 7.2441 billion = 7,244,100,000 people

**Assumption: Every person needs the calorie intake of a moderately active average adult male (age 30, 5’10”, 180 pounds)

- Calorie intake needed to maintain body weight: 2,500 calories per day, 912,500 calories per year
- Total calorie intake for entire world population: 1.811025 x 10^13 calories per day, 6.61024125 x 10^15 calories per year.

**Step 2: Calories in Corn**

**Assumption: Everyone’s diet consists of only corn. Even though this would not be feasible in an actual situation, it provides a simplified model of food production.

- Calories: 62.8 calories per ear of corn
- Ears of corn needed to sustain everyone for a year: 1.05258618631 x 10^14 ears of corn
- One acre of land can yield 18,000 ears of corn per year
- Amount of land available to grow corn on: 7.68 billion acres on Earth = 7,680,000,000 acres
- Maximum amount of corn produced: 1.3824 x 10^14 ears of corn per year
- Maximum amount of calories produced from maximum amount of corn: 8.681472 x 10^15 calories per year

**Step 3: Population Limit**

Based on this data, we were able to calculate the maximum population on Earth based on the current maximum production of corn. We concluded that the carrying capacity of Earth is **9.513941917 billion people**.

**Step 4: Population Growth Over Time**

Using the population limit from the previous step and the last 200 years of population growth data, we were able to calculate the equation of the graph that displays the logistic growth of the population.

Using the equations from sheets 3 and 4, we graphed two logistic graphs to see the growth of the world population. (Red graph is from sheet 3 and black graph is from sheet 4)

__Step 5: Arable Land__

**Assumption: Everyone’s diet still consists of only corn and the yield per acre of corn is constant over time.

- Arable land is being lost at the rate of approximately 38,610 square miles (24.7 million acres) per year = 24,700,000 acres per year
- We used the amount of arable land available to find the amount of corn produced per year, the maximum amount of calories from corn, and the maximum sustainable population.
- In 2015, there is 7,680,000,000 acres of arable land.
- We used the same data as we did in Steps 1 and 2 to determine the new sustainable population given that the amount of arable land is decreasing.

- Based on this data, a linear relationship can be determined for the sustainable population. The equation of the linear data set is:
- (y – 9513941917.81) = -30598224.658(x – 2015) (green line on graph below)

- Using this graph and the black logistic growth graph, we determined that with decreasing arable land and constant corn production, the population of the Earth will just be sustained in the year 2055. After 2055, the amount of food produced will not be enough for the calories required by the entire world population.

**Step 6: Technological Innovation**

**Assumption: Due to continuous farming innovation, every five years the yield of corn per acre increases by 5% of the preceding five year’s yield of corn. The amount of arable land is still decreasing as it was in Step 5.

- We plotted the points as shown in the graph below (orange line).

- We would never run out of food in this case because the rate of technological innovation is increasing the yield of corn faster than the rate at which arable land (therefore amount of corn) is lost.

**Step 7:**

**Assumption: Relationships between oil-producing nations and the rest of the world slowly deteriorate with no hope of reconciliation. As a result, despite the need of corn for consumption, the corn-producing nations of the world must switch machinery and vehicles over to ethanol. Every 5 years the percent of ethanol needed increases by 3% as gasoline becomes more scarce. More corn must be collected to convert into ethanol by the government. (Also assume that the amount of corn is based on decreasing amount of arable land and increasing amount of technology).

- We plotted the points as shown in the graph below (purple line).

- In 2085, the amount of food produced will just barely be able to support a population of about 8.466 billion people.
- (Due to the scale of this graph, it is difficult to see the new curve produced by the loss of corn to ethanol production. To see the data more clearly, please click on the link below.)

**Link to Desmos Graph:** https://www.desmos.com/calculator/lbgqzbt6uj

Based on our results, the most accurate conclusion comes from Step 7 with a prediction that after 2085, the amount of food produced will not be able to sustain the world population growth. However, this calculation is based on many assumptions and the future is always subject to change, therefore our number is just an estimate and not a definite conclusion.

Katelyn Ripley and Elena Silverberg

Works Cited: