Question

Suppose that you have the following conditional expression. (Assume that all the variables are properly declared.) \((0<\text { backyard } \& \& \text { backyard }<=5000) ?\) fertilizingCharges \(=40.00\) : fertilizingCharges \(=40.00+\text { (backyard }-5000) * 0.01\) a. What is the value of fertilizingCharges if the value of backyard is \(3000 ?\) b. What is the value of fertilizingCharges if the value of backyard is \(5000 ?\) c. What is the value of fertilizingCharges if the value of backyard is \(6500 ?\)

Short answer

a) 40.00 b) 40.00 c) 55.00

Step-by-step solution

Understand the Conditional Expression

The expression is a ternary conditional operator. It evaluates the condition \[0 < \text{backyard} \&\& \text{backyard} \leq 5000\]If true, it sets `fertilizingCharges = 40.00`. Otherwise, it sets \[\text{fertilizingCharges} = 40.00 + (\text{backyard} - 5000) \times 0.01\]

Evaluate for Backyard = 3000

Since 3000 is between 0 and 5000, the condition is true. Thus:\[\text{fertilizingCharges} = 40.00\]

Evaluate for Backyard = 5000

5000 is exactly at the upper boundary of the condition. Thus, the condition is also true and:\[\text{fertilizingCharges} = 40.00\]

Evaluate for Backyard = 6500

6500 is greater than 5000, so the condition is false. Calculate as follows:\[\text{fertilizingCharges} = 40.00 + (6500 - 5000) \times 0.01\]\[= 40.00 + 1500 \times 0.01 = 40.00 + 15.00 = 55.00\]

Key concepts

Ternary Operator

The ternary operator in C++ is a compact way of writing a simple if-else condition. It's often referred to as the conditional operator. Instead of writing a full if-else statement, one can use this operator to evaluate a condition and choose between two expressions based on whether the condition is true or false. The syntax is:

• condition ? expression_if_true : expression_if_false;

This can be particularly helpful in reducing code length and increasing readability when the expressions are short. In the given exercise, the ternary operator checks if the value of `backyard` lies between 0 and 5000. If true, it assigns `40.00` to `fertilizingCharges`. If not, it calculates `fertilizingCharges` based on the extra area beyond 5000 square units.

Expression Evaluation

Expression evaluation in programming refers to the calculation of the result of an expression. In C++, expressions are evaluated following the rules of precedence and associativity. To understand expression evaluation better, break down the expression step by step. For instance, in the exercise, when `backyard = 6500`:

• First, compute backyard - 5000 which is 1500;
• Then multiply the result by 0.01, yielding 15.00;
• Finally, add 40.00 to get the result of 55.00.

Intermediate calculations allow easier tracking of how each part of the expression contributes to the final result. This method enhances understanding and helps debug potential issues in more complex expressions.

Conditional Logic in Programming

Conditional logic is fundamental in programming, allowing programs to make decisions. It's the backbone of control flow, deciding which sections of code to execute based on given conditions. In this exercise, the logic checks whether the size of `backyard` is within a specific range. The C++ syntax uses comparison operators like >, <, and logical operators such as && to combine conditions. The compound condition 0 < backyard && backyard <= 5000 checks two things:

• Is `backyard` greater than 0?
• Is `backyard` less than or equal to 5000?

Both parts must be true for the compound condition to be true. If any part of the condition fails, the entire expression evaluates to false. Conditional logic, like this, provides flexibility, defining behavior for various data outcomes. It forms the scaffolding for more advanced decision-making in programming tasks.