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All content is created by qualified contributors and reviewed by the community. Our source-available approach means anyone can inspect materials and propose improvements. Practice exercises include explanations so you learn from mistakes, not just scores.

## From Paper to Pandemic Have you ever imagined folding a sheet of paper <InlineMath math="42 \text{ times}" />? If it were possible to do so, its thickness would exceed the distance from Earth to the Moon! This is because each fold doubles the thickness of the paper, this is what we call **exponential growth**. Exponential growth occurs when something increases by a constant multiplier in each time interval. In early <InlineMath math="2020" />, the world experienced a real example of exponential growth through the spread of the COVID-19 virus. One infected person could transmit to two people, then four, eight, and so on. ## Definition of Exponents An exponent is a shorthand way to write repeated multiplication. Imagine you are calculating how many people are infected with a virus like COVID-19. At each transmission phase, the number of infected people will increase in an interesting pattern: <BlockMath math="1 = 2^0 \quad 2 = 2^1 \quad 4 = 2 \times 2 = 2^2 \quad 8 = 2 \times 2 \times 2 = 2^3 \quad 16 = 2 \times 2 \times 2 \times 2 = 2^4" />

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Given the operation $\triangle(a, b) = ka + \frac{b}{m}$ where $k$ and $m$ are positive integers. If $\triangle(2, 4) = 8$ and $\triangle(3, 5) = 11$ , then the value of $\triangle(5, 9)$ is ....

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For the operation $\triangle(a,b)=ka+\frac{b}{m}$ , we know $\triangle(2,4)=8$ and $\triangle(3,5)=11$ . How do I find $\triangle(5,9)$ ?

Subtract the first equation from the second:

$k+\frac{1}{m}=3$

Because $k$ and $m$ are positive integers, $\frac{1}{m}$ can only be an integer when $m=1$ . That makes $k=2$ .

Put both values into the final operation:

$\triangle(5,9)=5(2)+\frac{9}{1}=19$

So $\triangle(5,9)=19$ .

Motion becomes easier to understand when you can see it for yourself

Horizontal component: $v_{0x}=20\text{ m/s}$
Vertical component: $v_{0y}=34.6\text{ m/s}$
Peak time: $t=3.5\text{ s}$
Flight time: $T=6.9\text{ s}$
Range: $R=138.6\text{ m}$
Velocity at two seconds: $\vec{v}=\langle 20, 14.6\rangle\text{ m/s}$

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From Paper to Pandemic

Have you ever imagined folding a sheet of paper $42 \text{ times}$ ? If it were possible to do so, its thickness would exceed the distance from Earth to the Moon! This is because each fold doubles the thickness of the paper, this is what we call exponential growth.

Exponential growth occurs when something increases by a constant multiplier in each time interval. In early $2020$ , the world experienced a real example of exponential growth through the spread of the COVID-19 virus. One infected person could transmit to two people, then four, eight, and so on.

Definition of Exponents

An exponent is a shorthand way to write repeated multiplication. Imagine you are calculating how many people are infected with a virus like COVID-19. At each transmission phase, the number of infected people will increase in an interesting pattern:

1 = 2^0 \quad 2 = 2^1 \quad 4 = 2 \times 2 = 2^2 \quad 8 = 2 \times 2 \times 2 = 2^3 \quad 16 = 2 \times 2 \times 2 \times 2 = 2^4

Agent

Open .md

## From Paper to Pandemic

Have you ever imagined folding a sheet of paper <InlineMath math="42 \text{ times}" />? If it were possible to do so, its thickness would exceed the distance from Earth to the Moon! This is because each fold doubles the thickness of the paper, this is what we call **exponential growth**.

Exponential growth occurs when something increases by a constant multiplier in each time interval. In early <InlineMath math="2020" />, the world experienced a real example of exponential growth through the spread of the COVID-19 virus. One infected person could transmit to two people, then four, eight, and so on.

## Definition of Exponents

An exponent is a shorthand way to write repeated multiplication. Imagine you are calculating how many people are infected with a virus like COVID-19. At each transmission phase, the number of infected people will increase in an interesting pattern:

<BlockMath math="1 = 2^0 \quad 2 = 2^1 \quad 4 = 2 \times 2 = 2^2 \quad 8 = 2 \times 2 \times 2 = 2^3 \quad 16 = 2 \times 2 \times 2 \times 2 = 2^4" />

Human

Open lesson

From Paper to Pandemic

Definition of Exponents

1 = 2^0 \quad 2 = 2^1 \quad 4 = 2 \times 2 = 2^2 \quad 8 = 2 \times 2 \times 2 = 2^3 \quad 16 = 2 \times 2 \times 2 \times 2 = 2^4

Agent

Open .md

## From Paper to Pandemic

Have you ever imagined folding a sheet of paper <InlineMath math="42 \text{ times}" />? If it were possible to do so, its thickness would exceed the distance from Earth to the Moon! This is because each fold doubles the thickness of the paper, this is what we call **exponential growth**.

Exponential growth occurs when something increases by a constant multiplier in each time interval. In early <InlineMath math="2020" />, the world experienced a real example of exponential growth through the spread of the COVID-19 virus. One infected person could transmit to two people, then four, eight, and so on.

## Definition of Exponents

An exponent is a shorthand way to write repeated multiplication. Imagine you are calculating how many people are infected with a virus like COVID-19. At each transmission phase, the number of infected people will increase in an interesting pattern:

<BlockMath math="1 = 2^0 \quad 2 = 2^1 \quad 4 = 2 \times 2 = 2^2 \quad 8 = 2 \times 2 \times 2 = 2^3 \quad 16 = 2 \times 2 \times 2 \times 2 = 2^4" />

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Start learning at your own pace

$0.00

Access to 5,000+ lessons

2,000+ practice exercises with explanations

Basic AI tutor (10 messages per day)

1 complete tryout for free

Community access on Discord

Start Learning

Pro

Practice more seriously with Nina, 3,000 monthly AI credits, and repeat tryout access.

$8.99

/month

Everything in Free, plus:

3,000 AI credits each month for premium Nina models

Start another tryout set or repeat a tryout, with IRT scoring on supported sets and detailed explanations

Download lessons as PDFs and listen to audio versions

Priority support when you need guidance

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From Paper to Pandemic

Definition of Exponents

From Paper to Pandemic

Definition of Exponents

We were students too. We know what it is like to choose between learning and eating. Core access is free. Always.

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Every school has different needs. We get it.

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Learn until it clicks.

Students from these schools and universities learn with Nakafa.

Learning doesn’t stop when you finish reading. Put it to the test with Tryout, see what still feels unclear, then ask Nina without starting over.

Start with the subject you need

After learning, see what you really understood

If you are still unsure, Nina already knows which part you mean

Motion becomes easier to understand when you can see it for yourself

You do not have to take our word for it. Follow the lesson back to its sources.

From Paper to Pandemic

Definition of Exponents

From Paper to Pandemic

Definition of Exponents

We were students too. We know what it is like to choose between learning and eating. Core access is free. Always.

Free

Pro

Free

Pro

Every school has different needs. We get it.

Still have questions?

Find people who get what you are learning

Free

Pro

Learn until it clicks.

Students from these schools and universities learn with Nakafa.

Learning doesn’t stop when you finish reading. Put it to the test with Tryout, see what still feels unclear, then ask Nina without starting over.

Start with the subject you need

After learning, see what you really understood

If you are still unsure, Nina already knows which part you mean

Motion becomes easier to understand when you can see it for yourself

You do not have to take our word for it. Follow the lesson back to its sources.

We were students too. We know what it is like to choose between learning and eating. Core access is free. Always.

Free

Pro

Every school has different needs. We get it.

Still have questions?

Is Nakafa really free?

What AI models can I use?

Can I download lessons for offline use?

What subjects and grades do you cover?

Is my data private?

Can schools use Nakafa?

How does Nakafa ensure content accuracy?

Find people who get what you are learning

Learn until it clicks.

Students from these schools and universities learn with Nakafa.

Learning doesn’t stop when you finish reading. Put it to the test with Tryout, see what still feels unclear, then ask Nina without starting over.

Start with the subject you need

After learning, see what you really understood

If you are still unsure, Nina already knows which part you mean

Motion becomes easier to understand when you can see it for yourself

You do not have to take our word for it. Follow the lesson back to its sources.

We were students too. We know what it is like to choose between learning and eating. Core access is free. Always.

Free

Pro

Free

Pro

Every school has different needs. We get it.

Still have questions?

Is Nakafa really free?

What AI models can I use?

Can I download lessons for offline use?

What subjects and grades do you cover?

Is my data private?

Can schools use Nakafa?

How does Nakafa ensure content accuracy?

Find people who get what you are learning

Free

Pro