Learning Objectives:

__Math Tutoring on Applications of First Order Differential Equations__

*Some of the important Applications of First Order Differential Equations are – *

*1. *__Exponential Growth or Uninhibited Growth & Exponential Decay:__

This models **Exponential Growth** which means the **rate of growth** is proportional to the population or amount. This can also be used to model **Continuous Interest.**

We will solve this differential equation to find ** P(t)**, but the only function that satisfies this is

If**,** the above model explains **Exponential decay**, which means the **rate of decline or decay** is proportional to the population or amount.

*2. *__Problems regarding Mixtures of Two Solutions:__

** A(t)** is the amount of the substance dissolved in the liquid in the tank at any time

Liquid is entering and leaving a tank. The liquid entering the tank will contain a different concentration of substance dissolved in it.

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*3. *__Newton’s Law of Cooling:__

The temperature **‘ T’** of a cooling object drops at a rate that is proportional to the difference

We will solve this differential equation to find *T***( t)**

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**Hook Question:**

*1. **Give some example of **Applications of First Order Differential Equations**.*

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