bill gets paid $20 just for accepting a yard job he then earns $3 for every hour spent pruning or weeding flowers. write a recursive function to model his total earnings at his job.
Y = 3x + 20.
def bill_earnings(hours):
if hours == 0:
return 20
else:
return 3 * hours + bill_earnings(hours-1)
# Testing the function
print(bill_earnings(0)) # Bill's earnings for 0 hours worked
print(bill_earnings(1)) # Bill's earnings for 1 hour worked
print(bill_earnings(5)) # Bill's earnings for 5 hours worked
To write a recursive function that models Bill's total earnings at his job, we can use the concept of recursion to break down the problem into smaller subproblems.
Here's an example of a recursive function in Python that models Bill's total earnings:
```python
def calculate_total_earnings(hours):
if hours == 0:
return 20 # Base case: The initial $20 for accepting the job
else:
return calculate_total_earnings(hours - 1) + 3 # Recursive case: Adding $3 for each hour spent
# Example usage:
total_earnings = calculate_total_earnings(10)
print("Bill's total earnings for 10 hours of work: $", total_earnings)
```
In this function, the base case occurs when `hours` equals 0, representing no additional hours of work. In this case, the function returns the initial $20 that Bill gets paid for accepting the job.
In the recursive case, the function calls itself with `hours - 1` as the argument, representing one less hour of work. The result is then added to the current call's total earnings for the previous hours.
By repeatedly calling the function with decreasing values of `hours`, the function eventually reaches the base case and returns the total earnings for all the hours of work.
You can pass any positive integer value of `hours` to the function to calculate Bill's total earnings for that many hours of work.
To write a recursive function that models Bill's total earnings at his job, we can break down the problem into smaller steps. We'll define a function called `calculateEarnings` that takes in the number of hours worked as a parameter. Here's how you can implement it in Python:
```python
def calculateEarnings(hours):
if hours == 0:
return 20
else:
return calculateEarnings(hours - 1) + 3
```
Let me explain how this recursive function works:
1. The base case is when `hours` is equal to 0. In this case, it means no hours were worked, so we simply return the fixed amount of $20 that Bill gets paid for accepting the job.
2. For any other value of `hours`, the function is called recursively by subtracting 1 from `hours` and adding the earnings for that hour using the formula `calculateEarnings(hours - 1) + 3`. This means we calculate the earnings for the previous hour and add $3 to it.
By calling this recursive function with the number of hours worked, you will get Bill's total earnings at his job. For example, if you want to know his earnings after working for 5 hours, you can call `calculateEarnings(5)`.