1. The problem gives a differential equation describing the rate of change of $N(t)$: $$\frac{dN}{dt} = N \cdot \left(90000 - \frac{3N}{20000}\right)$$ and an initial condition or value $N = 20000000$ (20 million trucks). 2. This is a logistic-type differential equation where the growth rate depends on $N$ itself. 3. To analyze or solve it, first rewrite the equation: $$\frac{dN}{dt} = 90000N - \frac{3N^2}{20000}$$ 4. Simplify the second term: $$\frac{3N^2}{20000} = 0.00015 N^2$$ So, $$\frac{dN}{dt} = 90000 N - 0.00015 N^2$$ 5. This equation models growth with a carrying capacity. The carrying capacity $K$ is found by setting $\frac{dN}{dt} = 0$: $$90000 N - 0.00015 N^2 = 0$$ $$N(90000 - 0.00015 N) = 0$$ So either $N=0$ or $$90000 - 0.00015 N = 0 \Rightarrow N = \frac{90000}{0.00015} = 600000000$$ 6. The carrying capacity is $600000000$ trucks. 7. The initial value $N=20000000$ is below the carrying capacity, so the population will grow towards $600000000$ over time. 8. To solve explicitly, separate variables and integrate, but since the problem does not request explicit solution, this analysis suffices. Final answer: The carrying capacity of the system is $600000000$ trucks, and the population $N(t)$ grows according to the logistic differential equation given.