High School

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

- The first week, the dealership sold one car ([tex]P_0 = 1[/tex]).
- The second week, the dealership sold four cars ([tex]P_1 = 4[/tex]).

1. Write the recursive formula for the number of cars sold, [tex]P_N[/tex], in the [tex](N+1)[/tex]th week.
[tex]P_N = P_{N-1} + 3[/tex]

2. Write the explicit formula for the number of cars sold, [tex]P_N[/tex], in the [tex](N+1)[/tex]th week.
[tex]P_N = 3N + 1[/tex]

3. If this trend continues, how many cars will be sold in the fourth week?

Answer :

The recursive formula is PN = PN-1 + 3. The explicit formula is PN = 3N + 1. In the fourth week (N = 3), 10 cars will be sold.

Recursive formula for the number of cars sold, PN, in the (N+1)th week: PN = PN-1 + 3

Explicit formula for the number of cars sold, PN, in the (N+1)th week: PN = 3N + 1

To find the number of cars sold in the fourth week (N = 3), plug in N = 3 into the explicit formula:

PN = 3 * 3 + 1 = 9 + 1 = 10

So, if the trend continues, 10 cars will be sold in the fourth week.

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