Question

Question 9

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A banking firm uses an algorithm d =(n −45)² + 450 to create models given
several data entries, n, where d represents delay measured in seconds per data entry.
For how many data entries does the algorithm have the least delay?
a. 30
b. 40
c. 45
d. 50

Answer 1

C


To determine the number of data entries for which the algorithm has the least delay, we need to find the minimum value of d.

The equation given is d = (n - 45)² + 450. We can start by expanding the squared term:

d = n² - 90n + 2025 + 450
d = n² - 90n + 2475

To find the minimum value of d, we can take the derivative with respect to n and set it equal to zero:

d/dn (n² - 90n + 2475) = 2n - 90 = 0
2n = 90
n = 45

Therefore, the minimum value of d occurs when n = 45. This means that for any number of data entries other than 45, the delay will be greater.

Therefore, the answer to the question is option c. The algorithm has the least delay for 45 data entries.