1. The problem asks which graph represents the solution to the logistic differential equation $$\frac{dP}{dt} = P \cdot \left(2 - \frac{P}{10}\right).$$ 2. This is a logistic growth model with growth rate 2 and carrying capacity 10 (since the term $$2 - \frac{P}{10}$$ becomes zero when $$P=20$$, but note the factor inside is $$P/10$$, so carrying capacity is $$20$$ because $$2 - \frac{P}{10} = 0 \Rightarrow P = 20$$). 3. The logistic equation solutions start near zero, grow exponentially at first, then slow down and level off at the carrying capacity. 4. Graph A and C show exponential growth without leveling off, so they cannot be logistic solutions. 5. Graph B levels off at $$P=15$$, which is not the carrying capacity 20, so it is not the correct solution. 6. Graph D starts near zero, rises steeply, and levels off at $$P=20$$, matching the carrying capacity from the equation. 7. Therefore, the correct graph representing the logistic differential equation solution is Graph D. Final answer: Graph D