### Section 3: Equation Components

#### The “Unused Portion of K”

Notice that the **logistic equation** looks like the **exponential equation** multiplied by **[1-(N/K)]**. This mathematical term is what accounts for the **density-dependent population growth rate**.

Lake divided into 50 equally sized squares with each square that can only support one fish on average.

Notice that the **logistic equation** looks like the **exponential equation** multiplied by **[1-(N/K)]**. This mathematical term is what accounts for the **density-dependent population growth rate**.

This gives the **per capita growth rate** of the population, which is represented as:

The **per capita growth rate** is mathematically interchangeable with the variable **r (realized intrinsic rate of increase)**. **r** is the rate of increase at each moment in time. Therefore:

Given this equation for **r**:

Predict what happens to r as the population reaches K.

If K = 50 and r_{max} = 0.5, when will r be exactly half of r _{max}?

**r** will be exactly half of ** r _{max} ** when

**N**equals:

**Number of Fish (N)**