The third lesson in Wasteland Survival with Doctor Albert will again focus on the important topic of food. In our previous lessons, we focused on hunting for food. However, in the end of Mole rat hunt-Part 2 WSDA we saw that this can be quite perilous if we are not extremely careful. Therefore, we will look at a more sustainable source of food: farming.

**Location**

While hunting for food, you will necessarily be mobile in your daily life. There will be certain locations you can revisit, but you can’t just sit in one spot. However, when you begin farming, your mobility will be extremely limited. It is much more work to tear down and replant on entire field than it is to take down your tent. Because of this, you need to be strategic your choice of farmland.

For my farm, I chose a location close to a river that had enough land to plant in. I also chose a place close to a nuclear power plant. While the first choices are for obvious reasons, the last choice may not seem to be wise. When I first left the vault, I assumed that the radiation would kill anything living, thus leading to an infertile land around the plant. However, any plants or animals that were negatively affected by the radiation have already died out in the fallout that followed the bombs. The crops that are left to plant are therefore the ones that have thrived under the affects of radiation. This has made my swath of land very fertile.

**Crops**

As we just alluded to, many crops that were available before the great war are no longer around. Some of those that were around, became mutated to the point that they would be considered a new species of plants.

The plants available to plant that survived the fallout are

- blackberries,
- carrots
- corn,
- pumpkins,
- melons.

The mutated crops we have are

- mutfruit,
- razorgrain,
- tatos.

Pictures of the available crops are below in the order written above.

When you make your choice of crop to grow, it may be that you have to grow the first plant that you are able to find. You, therefore, may not have much of a choice. Eventually, if you continue to scour the wasteland, you should find each of these growing somewhere, allowing you to bring a sample back to your farm. Eventually, I would suggest planting different crops. This will help not only your nutrition, but it will also provide some variety to your taste buds. For this lesson, I will stick with a crop most people are comfortable with, corn.

**Planting**

When you first find a cornstalk, your mouth will begin to water, your stomach will growl with anticipation and you will want nothing more to tear into the corn and satisfy your hunger. In fact, for quite a while I did just this. It is difficult to think about the future when you are hungry. I would highly encourage you not to make this mistake, or at least to only make it a dozen or so times.

When you are finally able to overcome this desire to eat the plant, you will need to take it back to your chosen farming location. Now, plant it in the ground. If you had experience farming or gardening prior to the war, you may laugh at how easy I make this sound. However, it is now legitimately that easy. You throw the corn and some fertilizer on the ground, and there is suddenly a cornstalk in front of you.

The hard part is now that you have to wait for the cornstalk to mature and produce more food. During this waiting period, it is best to keep yourself busy. I would suggest hunting in order to find food so that you aren’t tempted to eat the cornstalk itself, but you can also go about any thing else you may need to get done.

**Harvesting**

Then, a few months later, if the bugs, deer, or other things don’t get into your corn, there would be corn on your cornstalk. At least, that’s how it was before all this radiation. Now, the bugs and deer are more likely to eat you than your corn. Also, the corn has been so mutated that it no longer takes months to grow. Instead, it takes three hours.

Yes, I said that correctly, it will take 3 hours for a newly planted stalk to produce corn. All of you that doubted the radiation would help my corn grow, you can chew on that while I eat my corn!

It isn’t quite time yet to eat my corn though. Three hours is not a long time for corn to grow, but you can’t live off of one ear of corn every three hours. If you can sate your hunger with something else, you can instead replant this ear of corn. This will then give you two corn stalks.

**How long until I can eat?**

I know it is ever more tempting to eat the corn you’ve grown. We will, however, grow enough corn that we will be able to feed ourselves entirely from our crop. In my case, I found that if I ate eight ears of corn every three hours, I wouldn’t need any other food. You may have different needs, depending on how much you eat, if you have others with you, or if you are supplying food for a settlement. We will work through how to determine how long you will need to wait before you are able to have a sustainable food source for a few of these situations.

**Sequence**

In order to determine how much corn we will have after a given amount of time, we will construct a sequence. We will then use the pattern we find in order to determine the general term in the sequence. If we let \(c_{n}\) be the number of cornstalks after \(n\) 3-hour periods, our sequence will look like

- \(c_{0}=1\), since we have just planted the first stalk at time 0.
- \(c_{1}=2\). Here we have the original stalk, plus we planted the new cornstalk.
- \(c_{2}=4\). We have two from the previous time period. Each of these gave us a new ear of corn, which we then planted and turned into a cornstalk.
- \(c_{3}=8\).

Instead of explaining how we got \(c_{3}=8\), I hope you will be able to follow the pattern from the previous examples and figure this out. Please try to work this out.

After looking over this pattern, we will note that every three hours we will double the amount of corn. Therefore, if we want to find the amount of corn after \(n\) 3-hour periods, we would take \((1*2*2*2 \ldots*2)\) where there are \(n\) \(2\)s. If we simplify this notation, we get \(c_{n}=2^{n}\).

**How long then?**

I need 8 ears of corn every 3 hours. If I want to find how long I will have to wait, I simply solve the following equation \[\begin{align*} 2^{n}&=8 \\ log_{2}(2^{n})&=\log_{2}(8) \\ n&=3. \end{align*}\] Recall that the logarithmic function is the inverse of the exponential, so we will need this to solve for \(n\). Now, since there are still calculators, you can find one and solve for \(n\), or you can just realize that \(2^{3}=8\), so \(\log_{2}(8)=3\). Therefore, I will have to wait three 3-hour periods before I will have enough corn planted to ensure that I can feed myself. That is, I will have to wait 9 hours before I no longer have to worry about hunting for food. This is quite the remarkable finding, as even if you are starving, you should be able to make it 9 hours by hunting instead of eating your corn.

On the other hand, let’s suppose that you had 100 people in a settlement that you were trying to feed. If each of these people needed eight ears of corn every three hours, you would need to have planted 800 ears of corn. Before finding this solution, I want to note a couple of things.

- In the first case, we only had eight ears of corn, so we only had new corn every three hours.
- If we have a large enough number of corn, we can work under the assumption that new corn will constantly be available at a rate that will result in a doubling every three hours.

Therefore, if we let \(t\) be the number of hours, we can say that the corn available after a given amount of time \(t\) is \(c(t)=2^{\frac{t}{3}}\). According to this model, we would have \(2^{\frac{1}{3}}\) \approx 1.26\) ears of corn after 1 hours. This doesn’t make sense in the context of our problem. However, when we look at larger value of \(t\), we will quickly move from one whole number to the next. This will result in a more natural interpretation of the results.

Making use of this formula, we will find \[\begin{align*} 2^{\frac{t}{3}}&=800 \\ \frac{t}{3}&=\log_{2}(800) \\ t&=3\log_{2}(800) \\ t& \approx 28.9.\end{align*}\] It will therefore take 28.9 hours before you have enough corn planted to feed a settlement of 100 people. Considering how many people you will be able to feed, this really isn’t that long of a time to have to keep everyone from eating the corn. However, I don’t envy the guy that has to tell the hungry people they can’t eat the delicious looking corn for the next 28.9 hours.

Now, is 800 cornstalks enough to assume continuous growth? Probably not, so you will likely have to wait until the 30 hour period before you actually have enough corn. However, I wanted to use this as an example as the technique is more easily generalized if you want to work with a town of 1000, or a city of 10 million.

**Conclusion**

As a final remark, it would only take around 3 days and 8 hours to have enough corn planted for a city of 10 million. Herein lies the utility of farming. As long as you can abstain from eating your initial crops, you will quickly have enough food to feed even the largest of populations. Since we hope to help humanity thrive in this new world, we will have a much easier time doing so if we can keep the people fed.

I hope you learned something from this. If you did, make sure to share the post or the video on social media. We really appreciate you spreading the word about math survival.