Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A software engineer is designing an algorithm where the processing time T (in milliseconds) for n data points is given by T(n) = 2n^2 - 5n + 3. What is the difference in processing time between 5 data points and 3 data points?
- A48 ms
- B28 ms
- C32 ms
- D18 ms
Show answer & explanationAnswer & explanation
Correct answer: B. 28 ms
First, calculate T(5) = 2(5)^2 - 5(5) + 3 = 2(25) - 25 + 3 = 50 - 25 + 3 = 28. Next, calculate T(3) = 2(3)^2 - 5(3) + 3 = 2(9) - 15 + 3 = 18 - 15 + 3 = 6. The difference is T(5) - T(3) = 28 - 6 = 22.
Why the other options are wrong
- A. Incorrect. This would be T(5) if the coefficient of n^2 was 3, or other calculation error.
- C. Incorrect. This would be if T(5) was 32 or T(3) was 0.
- D. Incorrect. This might be T(3) or an error in calculation.
Function Evaluation Difference
The numerical difference between the output values of a function when evaluated at two different input values.
- Evaluate the function for each given input separately.
- Subtract the smaller result from the larger result (or as specified).
- Ensure correct order of operations for each evaluation.
Memory trick: Think 'two separate calculations, then one subtraction' – like finding the change between two points on a graph.