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**Week 5: Differential. Growth and decay model. ( page 224, Exercise 3.7 , Exercise 3.8)**

The differential of a **function** is equal to the derivative of the **function** times the differential of the independent variable: dy=df(x)=f′(x)dx. The key concept of **exponential growth** is that the **population growth** rate —the number of organisms added in each generation—increases as the **population** gets larger. When **population** size, N, is plotted over time, a J-shaped **growth** curve is made.Systems that exhibit **exponential growth** follow a **model** of the form y=y0ekt. In **exponential growth**, the rate of **growth** is proportional to the quantity present. In other words, y′=ky. **Decay models** are applicable on data sets where data items are associated with points in a metric space (locations) and there is a notion of “significance” of a data item to a location, which **decays** (decreases) with the distance between the item and the location. This decrease is modeled by a **decay** function.