Question

The cost of renting a kayak for one
hour is $23. Each additional hour
is $8 more. Write the formulas to
represent the situation.
explicit formula:
recursive formula:

Answer 1

To represent the situation of renting a kayak with an explicit formula and a recursive formula, we can start by defining what we have:

1. **Base Cost for the First Hour**: \( C(1) = 23 \)
2. **Cost for Each Additional Hour**: The cost for each additional hour after the first hour is $8.

### Explicit Formula

The explicit formula for the cost \( C(n) \) of renting the kayak for \( n \) hours can be defined as follows:

\[
C(n) = 23 + 8 \times (n - 1)
\]

This formula states that for the first hour, you pay $23 and for each subsequent hour (from the second hour onward), you pay an additional $8.

### Recursive Formula

The recursive formula is defined based on the cost of the previous hour. It can be written as:

\[
C(1) = 23
\]
\[
C(n) = C(n - 1) + 8 \quad \text{for } n > 1
\]

In this recursive formula, \( C(1) \) is the cost for the first hour, and for every hour \( n \) greater than 1, the cost is equal to the cost of the previous hour plus $8.

### Summary

- **Explicit Formula**: \( C(n) = 23 + 8 \times (n - 1) \)
- **Recursive Formula**:
- \( C(1) = 23 \)
- \( C(n) = C(n - 1) + 8 \) for \( n > 1 \)