Question

Write the definition of a function that takes as input three decimal numbers and returns the first number multiplied by the second number to the power of the third number.

Short answer

Define `compute_result(a, b, c)` that returns `a * (b ** c)`.

Step-by-step solution

Define the Function Signature

First, we need to decide on the function's signature, which includes the name of the function and its parameters. Let's call the function `compute_result`, and it will take three inputs: `a`, `b`, and `c`, which are all decimal numbers.

Apply the Power Operation

Inside the function, the first operation is to raise the second number, `b`, to the power of the third number, `c`. This can be done using the exponentiation operator `**` in Python: `b ** c`.

Multiply the Result

Next, multiply the first number, `a`, by the result from the previous step. This will look like: `a * (b ** c)` in the implementation.

Return the Result

Finally, the function should return the computed result. Use the `return` statement to provide the final value: `return a * (b ** c)`.

Complete Function Definition

Here is the complete definition of the function based on the steps above: ```python def compute_result(a, b, c): return a * (b ** c) ```

Key concepts

Function Signature

In C++, a function signature is a crucial component of defining a function. It consists of the function's name and its parameter list. In this context, the function was named `compute_result`. This name is followed by parentheses that contain the parameters, which for our problem include three decimal numbers: `a`, `b`, and `c`. While creating a function, it’s important to ensure that the signature clearly represents its purpose and the tasks it undertakes. Parameters should be descriptively named to indicate their roles. This practice helps others understand what values they need to pass when calling the function.

For good practice, other important details include specifying types for the parameters and return values, especially in languages like C++ where type safety is more rigid than in Python. This ensures that the function is used correctly by making sure all inputs and outputs adhere to expected data types.

Exponentiation

Exponentiation is a mathematical operation involving two numbers, the base and the exponent. In our problem, `b ** c` represents `b` (the base number) raised to the power of `c` (the exponent). In C++, this is not done with the `**` operator as in Python. Instead, it requires a function such as `pow()` from the `` library.

Exponentiation can solve a variety of problems, especially those involving growth rates or expansions. When implementing this in C++, it is vital to include the appropriate header file and use the `pow` function correctly to avoid unintended results. This helps facilitate complex calculations by converting them into manageable operations through the use of base and exponent concepts.

Return Statement

The return statement in C++ is used to output the result of a function back to the caller. In our function, `return a * (b ** c)` conveys that the computed result of multiplying `a` by `b` raised to the power `c` is sent back as the output of the function. The return statement not only ends the function's execution but also passes the calculated value to the caller, which can then be used further in the program.

Incorporating the return statement effectively ensures that functions provide useful and expected outputs. It is usually located at the end of the function definition and can be paired with calculations or straightforward values, returning either primitive types or complex objects.

Function Definition Steps

Defining a function involves a series of logical steps designed to implement its purpose. First, you determine the function signature, which establishes the name and parameters required. For example, `compute_result` accepts `a`, `b`, and `c`. These parameters guide the function's logic.

Next, you implement the core logic—in this case, performing exponentiation and multiplication. Breaking down tasks into smaller steps like this clarifies the operations for programmers and improves code readability. After the operations, the result must be returned using the syntax `return ...`, ensuring the function delivers its intended outcome.

Completing these steps systematically guarantees that the function is correctly implemented, making it easily reusable and maintainable in larger projects. Remember, clarity and thoroughness during definition minimize errors and aid in future modifications.