Question

Suppose that overspeed and fine are double variables. Assign the value to fine as follows: If \(0<\) overspeed \(<=5,\) the value assigned to fine is \(\$ 20.00 ;\) if \(5<\) overspeed \(<=10,\) the value assigned to fine is \(\$ 75.00\) if \(10<\) overspeed \(<=15,\) the value assigned to fine is \(\$ 150.00 ;\) if overspeed \(>15,\) the value assigned to fine is \(\$ 150.00\) plus \(\$ 20.00\) per mile over 15

Short answer

Determine the overspeed range and assign the fine accordingly. Calculate additional charges for overspeed greater than 15.

Step-by-step solution

Check Overspeed Range

First, determine which range the variable `overspeed` falls within. There are four possible ranges: \(0 < \text{overspeed} \leq 5\), \(5 < \text{overspeed} \leq 10\), \(10 < \text{overspeed} \leq 15\), and \(\text{overspeed} > 15\).

Assign Fine Based on Range

Based on the range identified: - If \(0 < \text{overspeed} \leq 5\), assign \(\text{fine} = 20.00\). - If \(5 < \text{overspeed} \leq 10\), assign \(\text{fine} = 75.00\). - If \(10 < \text{overspeed} \leq 15\), assign \(\text{fine} = 150.00\).

Calculate Fine for Overspeed > 15

If \(\text{overspeed} > 15\), calculate the fine as \(150.00 + 20.00 \times (\text{overspeed} - 15)\). This accounts for the \(\\(150.00\) base fine plus \(\\)20.00\) for each mile over 15.

Key concepts

Assignment Operators

Assignment operators in programming are used to assign values to variables. In the context of the given exercise, we need to assign a value to the variable `fine` based on the speed limit violation, represented by `overspeed`.

Here, the assignment operator `=` is used to update the `fine` variable with a specific dollar amount. The logic is straightforward:

• If the speed is marginally over the limit, assign a smaller fine.
• If the speed is more excessive, assign a larger fine.

Understanding assignment operators is crucial, as they help in setting up conditions to handle various scenarios in programming effectively. By adjusting the assigned value according to set conditions, we can maintain a dynamic and responsive system.

Range Checking

Range checking is essential to ensure that data falls within the expected boundaries before proceeding with operations. In the exercise, `overspeed` is checked against multiple ranges to determine the appropriate fine.

For instance, the first check identifies if `overspeed` falls between 0 and 5. This range ensures only marginal violations receive the smallest fine. As the overspeed value increases beyond these limits, each new defined range checks for increasingly severe violations and allocates higher fines accordingly.

• Wonder why different ranges? It helps in punishing speed violations based on severity.
• The logic here makes sure that every possible `overspeed` value is covered.

Range checking not only aids in specification but also facilitates flexibility and error control in algorithms.

Algorithm Design

Designing an algorithm involves creating a logical flow to solve a problem efficiently. When deciding fines, the algorithm determines which action to take based on the `overspeed` value.

This problem's algorithm follows these basic steps:

• Check the `overspeed` value against defined speed ranges.
• Assign the correct fine according to the relevant range.
• Calculate additional fines if necessary.

The algorithm’s design ensures clarity and precision. By laying out conditions and results in clear steps, we can address any overspeed scenario effectively. Algorithm design often includes decisions about control structures—like conditional statements—that steer the execution based on certain inputs, which is a practice demonstrated well in this example.

Incremental Computation

Incremental computation refers to the process of calculating output based on parts of the input data, especially useful when dealing with ranges and conditions. In our example, incremental computation is used when `overspeed` exceeds 15.

At this point, the base fine is $150.00, and each mile beyond 15 incurs an extra fee. The calculation "grows" incrementally based on the overspeed beyond 15 miles per hour—multiplying the additional miles by $20.00 and adding this to the base fine.

• This ensures the fine increases logically rather than arbitrarily.
• Incremental computation is particularly useful for scenarios where input values can vary significantly.

Understanding incremental computation allows programmers to focus on logically extending results from initial conditions, ensuring efficiency and accuracy in computations.