Question

Outdoor World tents camping tents for $23 for one day, $31 for two days, $39 for three days, $47 for four days, and so on to a maximum of seven days. Which recursive function represents these prices?

Answer 1

The recursive function representing the prices for renting camping tents for a period of up to seven days is Pn = Pn-1 + 8 for n > 1, with an initial condition P1 = $23.

Step-by-step explanation:

The student is asking to define a recursive function for the prices of renting camping tents from Outdoor World for a period of one to seven days. In this problem, the price to rent a tent increases in a linear fashion with each added day, and we're asked to create a function that defines this increase recursively.

To come up with a recursive function, we first need to identify the recurring pattern in the pricing. Observing the provided prices, there is an increase of $8 for each additional day beyond the first:

• 1 day = $23
• 2 days = $23 + $8 = $31
• 3 days = $31 + $8 = $39
• And so on...

The recursive function can then be defined as follows:

Pn = Pn-1 + 8, for n > 1
where Pn is the price to rent the tent for n days and Pn-1 is the price to rent the tent for n-1 days.

The initial condition is P1 = $23, since the price for the first day is given explicitly.