APFIVE Limit of a Logistic Growth Model
The proportion of a bacteria culture relative to its maximum population, $$y$$, is modeled by the differential equation $$\frac{dy}{dx} = y(1-y)$$ with the initial condition $$y(0)=0.2$$. The table provides selected values for the solution $$y(x)$$. What is the value of $$\lim_{x \to \infty} y(x)$$?
| x | y |
|---|---|
| 0 | 0.20 |
| 1 | 0.35 |
| 2 | 0.55 |
| 3 | 0.73 |
| 4 | 0.86 |
| 5 | 0.95 |
A
The population grows without bound.
B
$$0$$
C
$$0.2$$ remains constant.
D
$$1$$
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