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Answer :
Final answer:
In Linear Growth the dealership sells an additional six cars each week. The recursive formula, which predicts the number of cars sold in the next week based on the previous week's sales, is Pn = Pn-1 + 6. The explicit formula, which predicts total sales after any given number of weeks, is Pn = 5 + 6*n. If the trend continues, 35 cars will be sold in the 6th week.
Explanation:
In this situation, the automobile dealership experiences linear growth in car sales. In the first week, five cars are sold (P0 = 5), and in the second week, eleven cars are sold (P1 = 11). The increase in sales from the first week to the second week is six cars (P1 - P0), so we can presume that the dealership sells an additional six cars each week.
The recursive formula for the number of cars sold in the (n + 1)th week is: Pn = Pn-1 + 6. What this means is that the number of cars sold in the current week is the number of cars sold in the previous week plus six.
The explicit formula for the number of cars sold in the ( n + 1 )th week is Pn = 5 + 6*n. This formula predicts the total number of cars sold after n weeks, given that the initial amount (P0) is 5 and the common difference (the number of extra cars sold each week) is 6.
Finally, to calculate how many cars will be sold in the 6th week if the trend continues, we can use either of the formulas. With Pn = 5 + 6*n, substituting 5 for n gives: P5 = 5 + 6*5 = 35.
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