Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium

A software engineer is optimizing an algorithm. The runtime T (in milliseconds) of the algorithm for processing n data points is given by T(n) = 3n^2 + 5n. What is the difference in runtime between processing 10 data points and 5 data points?

  1. A250 milliseconds
  2. B300 milliseconds
  3. C325 milliseconds
  4. D275 milliseconds
Show answer & explanation

Correct answer: A. 250 milliseconds

To find the difference in runtime, we first calculate the runtime for 10 data points, then for 5 data points, and finally subtract the two results.

Why the other options are wrong

  • B. This is T(10) = 350, not the difference.
  • C. This is a plausible distractor, possibly from an arithmetic error.
  • D. This might be a calculation error or a misinterpretation of the operations.

Function Evaluation and Difference

To find the difference between function values at two points, evaluate the function at each point separately and then subtract the results.

  • Substitute the first input value into the function.
  • Substitute the second input value into the function.
  • Subtract the two resulting output values.

Memory trick: Calculate Each, Then Subtract.

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