SOLUTION: The number of cars sold weekly by a new automobile dealership grows according to a linear growth model. The first week the dealership sold eight cars (P0=8). The second week the de

Question 1200984: The number of cars sold weekly by a new automobile dealership grows according to a linear growth model. The first week the dealership sold eight cars (P0=8). The second week the dealership sold nine cars (P1=9).
Write the recursive formula for the number of cars sold, PN, in the (N+1)th week.
PN= ____ PN−1+ _____

Write the explicit formula for the number of cars sold, PN, in the (N+1)th week.
PN= ___ N+ ____

If this trend continues, how many cars will be sold in the sixth week?
____ cars
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
since the number of cars sold each week is 1 more than the number of cars sold the previous week:

the recursive formula is p(n) = p(n-1) + 1
you have to know what p(n-1) is before you can find p(n)
for example, if p(n-1) is 8, then p(n) is 9.

the explicit formula is p(n) = n + p(0).
you do not need to know what p(n-1) is before you can find p(n).
you only need to know what p(0) is.

in this problem, p(0) is assumed to be 8.
if you want to know what p(3) is, you can't find it using the recursive formula because you don't know what p(2) is.

you can find it using the explicit formula, as long as you know what p(0) is.
when p(0) = 8, the explicit formula becomes p(n) = n + 8
when n = 3, the explicit formula tells you that p(3) = 3 + 8 = 11.

if you use the explicit formula to find p(2), then you can use the recursive formula to find p(3).
p(2) = 2 + 8 = 10
p(3) = p(2) + 1 = 10 + 1 = 11.

the number of cars sold in the 6th week would use the explicit fromula of p(n) = n + 8 to get p(6) = 6 + 8 = 14.

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