To solve the given problem, let’s break it into its components:

1. Recursive Formula: The problem indicates the dealership sold 2 cars in week 0 ($P_0 = 2$) and 7 cars in week 1 ($P_1 = 7$). The growth is linear. To find the recursive formula, calculate the weekly growth rate:

   $\text{Growth Rate} = P_1 - P_0 = 7 - 2 = 5$

   The recursive formula is: $P_N = P_{N-1} + 5$

2. Explicit Formula: The explicit formula uses the initial value ($P_0$) and the growth rate to directly find $P_N$ for any $N$:

   $P_N = P_0 + 5N$ Substituting $P_0 = 2$: $P_N = 2 + 5N$

3. Number of Cars in the Sixth Week: Using the explicit formula ($P_N = 2 + 5N$), substitute $N = 6$:

   $P_6 = 2 + 5(6) = 2 + 30 = 32$

Final Answers:

1. Recursive Formula: $P_N = P_{N-1} + 5$
2. Explicit Formula: $P_N = 2 + 5N$
3. Cars in Sixth Week: $32$

Would you like a further explanation of the steps? Here are five follow-up questions for you to explore:

1. How can you verify the growth rate in a recursive model?
2. What are the differences between recursive and explicit formulas?
3. How do linear models differ from exponential models in real-world scenarios?
4. Could this trend continue indefinitely in reality? Why or why not?
5. What happens to $P_N$ as $N \to \infty$?

Tip: When working with recursive formulas, always confirm the growth rate consistency with given data.