Question 1205120: The number of cars sold weekly by a new automobile dealership grows according to a linear growth model. The first week the dealership sold seven cars (P0=7). The second week the dealership sold fifteen cars (p1=15).
Write the recursive formula for the number of cars sold,
Pn, in the (N+ 1)th week.
Pn=Pn+ Blank
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?
blank cars
In each box, enter a single number. Do not leave any boxes blank (enter 1 or 0 as appropriate if necessary)
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850)   (Show Source):
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
The statement of the problem has (at least) three faults.
(1) "n" and "N" are used interchangeably to represent the same thing.
(2) The form "Pn=Pn+ Blank" is not appropriate for a recursive formula. In fact, if that form is correct, then "Blank" is 0.
(3) The form "Pn= N+" is not appropriate for an explicit formula.
Since the number sold in week 1 is P(0), the number sold in week (n+1) is P(n).
Part 1 -- recursive formula
The recursive formula for the number sold in week (n+1) tells the number sold as a function of the number sold in week n. The number sold in week n is P(n-1); and since the number sold increases by the same number 8 in each week, the recursive formula for the number sold in week (n+1) is
P(n)=P(n-1)+8
Part 2 -- explicit formula
The explicit formula for the number sold in week (n+1) is a linear equation in the form
y=mx+b
or, in this problem,
P(n)=mn+b
Since the number sold increases by 8 each week, m=8; and since P(0)=7, b=7 and the formula is
P(n)=8n+7
Part 3 -- number sold in week 6
The number sold in week 6 is
P(5) = 8(5)+7 = 47
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