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Answer :
Final answer:
This problem represents a linear growth pattern. The recursive formula is Pn = Pn-1 + 6 and the explicit formula is Pn = 3 + 6(n - 1). In the fourth week, the dealership is expected to sell 21 cars.
Explanation:
The given data represents a linear growth pattern because the dealership's car sales are increasing by a constant amount each week. The weekly increase of car sales is 9-3=6 cars per week. For a linear model, the recursive formula, which you can use to find the next week's car sales given the current week's car sales, can be written as: Pn = Pn-1 + 6, where Pn-1 is the number of cars sold the week before and n represents the current week.
The explicit formula, which gives the number of cars sold in any given week directly, can be written as: Pn = Po + d(n-1), where Po is the number of cars sold in the first week, d is the constant difference (6 cars per week in this case), and n is the week number itself.
Therefore, given that Po = 3, and d = 6, the explicit formula becomes: Pn = 3 + 6(n - 1). Applying this formula, for the fourth week, P4 = 3 + 6*(4 - 1) = 21 cars will be sold.
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Answer:
21
Step-by-step explanation:
Given that the number of cars sold weekly by a new automobile dealership grows according to a linear growth model.
Linear growth means rate of change of sales is constant i.e. slope = m = constant.
I week sales = 3
II week sales =9
So we can write as every week 6 cars would increase
i.e. [tex]P_{n+1} =P_n+6[/tex]
In IV week we can say
no of cars sold = 3+(4-1)6
= 21.
