## 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, $y$ $y = x^2$ |
---|---|

$1$ | $1$ |

$2$ | $4$ |

$3$ | $9$ |

$4$ | $16$ |

$5$ | $25$ |

$6$ | $36$ |

**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, $y$ $y = 2^x$ |
---|---|

$1$ | $1$ |

$2$ | $4$ |

$3$ | $8$ |

$4$ | $16$ |

$5$ | $32$ |

$6$ | $64$ |

**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"?