Exponential growth: How folding paper can get you to the Moon

Translator: Rizqi Nurul Akbar Reviewer: Lanny Yunita

How many times can you fold a piece of paper?

Berapa kali selembar kertas bisa dilipat?

Assume that one had a piece of paper that was very fine,

Anggap saja satu orang memiliki sepotong kertas yang halus,

like the kind they typically use to print the Bible.

jenis kertas yang biasanya digunakan untuk mencetak Alkitab.

In reality, it seems like a piece of silk.

Kenyataannya, ini seperti selembar sutra.

To qualify these ideas,

Untuk memenuhi kriteria ini,

let's say you have a paper

ada sebuah kertas

that's one-thousandth of a centimeter in thickness.

setebal seperseribu sentimeter.

That is 10 to the power of minus three centimeters,

Itu 10 pangkat minus tiga sentimeter,

which equals .001 centimeters.

yang setara dengan 0,001 sentimeter.

Let's also assume that you have a big piece of paper,

Anggap saja ada selembar kertas yang besar,

like a page out of the newspaper.

seperti selembar halaman koran.

Now we begin to fold it in half.

Lalu dilipat menjadi dua.

How many times do you think it could be folded like that?

Berapa kali kertas itu bisa dilipat?

And another question:

Dan pertanyaan lain,

If you could fold the paper over and over, as many times as you wish,

jika kertas bisa dilipat berulang-ulang sebanyak mungkin,

say 30 times,

misalkan 30 kali,

what would you imagine the thickness of the paper would be then?

bagaimana ketebalan kertas itu nantinya?

Before you move on,

Sebelum dilanjutkan,

I encourage you to actually think about a possible answer to this question.

pikirkanlah masak-masak kemungkinan jawaban pertanyaan ini.

OK.

Oke.

After we have folded the paper once,

Setelah dilipat satu kali,

it is now two thousandths of a centimeter in thickness.

tebalnya menjadi 0,002 cm.

If we fold it in half once again,

Jika dilipat setengah lagi,

the paper will become four thousandths of a centimeter.

tebalnya akan menjadi 0,004 cm.

With every fold we make, the paper doubles in thickness.

Dari setiap lipatan, ketebalan kertasnya berlipat ganda.

And if we continue to fold it again and again,

Dan jika terus dilipat,

always in half, we would confront the following situation

selalu dilipat setengah, akan muncul situasi berikut,

after 10 folds.

setelah 10 kali lipatan.

Two to the power of 10,

Dua pangkat 10,

meaning that you multiply two by itself 10 times,

artinya dua dikalikan dua sebanyak 10 kali

is one thousand and 24 thousandths of a centimeter,

adalah 1,024 cm,

which is a little bit over one centimeter.

satu sentimeter lebih sedikit.

Assume we continue folding the paper in half.

Jika terus dilipat menjadi dua,

What will happen then?

apa yang akan terjadi?

If we fold it 17 times,

Jika dilipat 17 kali,

we'll get a thickness of two to the power of 17,

akan didapatkan ketebalan dari dua pangkat 17,

which is 131 centimeters,

sama dengan 131 cm,

and that equals just over four feet.

hampir sama dengan empat kaki.

If we were able to fold it 25 times,

Jika dilipat 25 kali,

then we would get two to the power of 25,

maka akan didapatkan dua pangkat 25,

which is 33,554 centimeters,

yaitu 33.554 sentimeter,

just over 1,100 feet.

hampir 1.100 kaki.

That would make it almost as tall as the Empire State Building.

Hampir setinggi Gedung Empire State.

It's worthwhile to stop here and reflect for a moment.

Mari berhenti di sini dan merenung sejenak.

Folding a paper in half, even a paper as fine as that of the Bible,

Melipat kertas yang bahkan sehalus kertas Alkitab menjadi dua,

25 times would give us a paper almost a quarter of a mile.

kemungkinannya 25 kali kertas itu akan menjadi hampir seperempat mil.

What do we learn?

Apa yang kita pelajari?

This type of growth is called exponential growth,

Jenis pertumbuhan ini disebut pertumbuhan eksponensial,

and as you see, just by folding a paper

dan bisa terlihat, hanya dengan melipat kertas

we can go very far, but very fast too.

jarak yang jauh bisa ditempuh, juga dengan sangat cepat.

Summarizing, if we fold a paper 25 times,

Artinya, jika kertas dilipat 25 kali,

the thickness is almost a quarter of a mile.

ketebalannya hampir seperempat mil.

30 times, the thickness reaches 6.5 miles,

Jika dilipat 30 kali, ketebalannya mencapai 6,5 mil,

which is about the average height that planes fly.

yaitu setara dengan ketinggian pesawat terbang.

40 times, the thickness is nearly 7,000 miles,

Jika dilipat 40 kali, ketebalannya hampir 7.000 mil,

or the average GPS satellite's orbit.

atau setara dengan orbit satelit GPS.

48 times, the thickness is way over one million miles.

Jika dilipat 48 kali, ketebalannya lebih dari satu juta mil.

Now, if you think that the distance between the Earth and the Moon

Jika jarak antara bumi dan bulan

is less than 250,000 miles,

adalah kurang dari 250.000 mil,

then starting with a piece of Bible paper

mulailah dengan selembar kertas Alkitab,

and folding it 45 times, we get to the Moon.

lipatlah 45 kali, maka bisa sampai ke bulan.

And if we double it one more time,

Dan jika digandakan sekali lagi,

we get back to Earth.

bisa kembali ke bumi.