## Story

**Virologist:**
It is a virus.

It is highly contagious.

It is spreading so fast.

**Mathematician:**
GOD help us!

How fast is it spreading?

**Statistician:**
On the first day (Day $1$), two people contacted it.

On the second day (Day $2$), four people contacted it.

On the third day (Day $3$), nine people contacted it.

On the fourth day (Day $4$), sixteen people were affected.

On the fifth day (Day $5$), twenty five people were affected.

On the sixth day (Day $6$), thirty six people were affected.

On the seventh day, (Day $7$), forty nine people tested positive for the virus.

*
Teacher: If this trend continues, how many people are likely to be infected on the ninth day?
What type of function does this scenario represent?
What is the graph of that function called?
*

On the ninth day, $81$ people are likely to be infected.

This represents a

**Quadratic function.**

The graph of a quadratic function is called a parabola.

Can we represent this information in a table?

Day, $x$ | Number of People, $y$ $y = x^2$ |
---|---|

$1$ | $1$ |

$2$ | $4$ |

$3$ | $9$ |

$4$ | $16$ |

$5$ | $25$ |

$6$ | $36$ |

$7$ | $49$ |

**Social Worker:**
Wait a minute!

We have an updated report.

Here it is:

On the first day (Day $1$), two people contacted it.

On the second day (Day $2$), four people contacted it.

On the third day (Day $3$), eight people contacted it.

On the fourth day (Day $4$), sixteen people were affected.

On the fifth day (Day $5$), thirty two people were affected.

On the sixth day (Day $6$), sixty four people were affected.

On the seventh day, (Day $7$), one hundred and twenty eight people tested positive for the virus.

*
Teacher: If this trend continues, how many people are likely to be infected on the ninth day?
What type of function does this scenario represent?
*

On the ninth day, $512$ people are likely to be infected.

This represents an

**Exponential function.**

Can we represent this updated information in a table?

Day, $x$ | Number of People, $y$ $y = 2^x$ |
---|---|

$1$ | $1$ |

$2$ | $4$ |

$3$ | $8$ |

$4$ | $16$ |

$5$ | $32$ |

$6$ | $64$ |

$7$ | $128$ |

**Teacher:** Do you see the difference between a **Quadratic Function** and an **Exponential Function**?

Do you see the difference between $x^2$ and $2^x$?

**Students:** Yes Sir/Ma'am.

**Teacher:** Can you mention some life scenarios of "Exponential Growth - increasing at a fast rate" and
"Exponential Decay - decreasing at a fast rate"?