The problem involves determining the domain of the function $R(t) = 2\sqrt{t} - t^3$. We are tasked with finding the correct domain $D$ from the given choices.

Step-by-step solution:

1. The function $R(t) = 2\sqrt{t} - t^3$ contains a square root $\sqrt{t}$.

   • The square root is defined only when its argument is non-negative, meaning $t \geq 0$.

2. The cubic term $-t^3$ is defined for all real values of $t$. However, the restriction comes from the square root term.

3. Therefore, the domain $D$ is determined by the condition $t \geq 0$, since $\sqrt{t}$ is only defined for non-negative $t$.

Thus, the domain of $R(t)$ is $D = [0, +\infty)$.

Correct answer:

The correct choice is $D = [0, +\infty)$.

Would you like further details or explanations?

Here are 5 related questions to expand your understanding:

1. How do we determine the domain of more complex functions with multiple terms?
2. What are the steps to find the domain of a function involving both square roots and polynomials?
3. How do we handle domains for functions with both rational and radical expressions?
4. What happens to the domain if there are additional terms inside the square root?
5. How does the behavior of a cubic term affect the overall domain of a function?

Tip: Always look out for square roots, logarithms, or divisions by variables when determining the domain of a function!