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The number of cars sold weekly by a new automobile dealership grows according to a linear growth model.

- The first week, the dealership sold six cars \((P_0 = 6)\).
- The second week, the dealership sold thirteen cars \((P_1 = 13)\).

Answer :

Final answer:

The linear growth model for the number of cars sold weekly by the new automobile dealership can be expressed as P_n = 7n - 1, where 'n' represents the week number.

Explanation:

To establish a linear growth model for the number of cars sold weekly by the automobile dealership, we can use the given information about the first and second weeks' sales. In the first week, the dealership sold six cars, so we can write this as P_1 = 6. In the second week, they sold 13 cars, which can be represented as P_2 = 13.

To find the linear equation for this growth, we need to calculate the common difference between consecutive weeks. In this case, the common difference is 13 - 6 = 7. This means that the number of cars sold increases by 7 each week. We can express this as a linear equation: P_n = 7n - 1, where 'n' represents the week number.

Therefore, the linear growth model for the number of cars sold weekly is P_n = 7n - 1. This equation allows us to predict the number of cars sold in any given week.

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