A botanist is cultivating a rare species of plant in a controlled environment and currently has 3000 of these plants. The population of this species that the botanist expects to grow next year, `N_("next year")`, can be estimated from the number of plants this year, `N_("this year")`, by the equation below.
`N_("next year")=N_("this year")+0.2(N_("this year"))(1-(N_("this year"))/(K))`
The constant K in this formula is the number of plants the environment is able to support.
The botanist would like to increase the number of plants that the environment can support so that the population of the species will increase more rapidly. If the botanist’s goal is that the number of plants will increase from 3000 this year to 3360 next year, how many plants must the modified environment support?

Explanation

To find the number of plants that the modified environment must support (K) for the botanist's goal of increasing the plant population from 3000 to 3360, we will use the given equation:

\[ N_{\text{next year}} = N_{\text{this year}} + 0.2(N_{\text{this year}})\left(1 - \frac{N_{\text{this year}}}{K}\right) \]

### Step-by-Step Solution:

1. **Identify the Known Values**:
- \( N_{\text{this year}} = 3000 \)
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