PLEASE EXPLAIN WHY/SHOW ANY WORK. Thank you :)

3. (10 points total - 2 points for each part (a)-(e), part (f) is optional) In this problem, we wish to compare the time taken to perform an algorithm on an input of size n versus on an input of size 4n. We saw that the exact time will vary with environmental factors such as hardware and software details, but t expect the time to scale when we increase the input size. For each function below, suppose we are running an algorithm of that order (i.e. in that class) on an input of size n then again on an input of size 4n. By what multiplicative factoir do we expect the total run-time of our algorithm to increase? For example, an answer of 3 means that we expect our algorithm to take 3 times as long on an input of size 4n versus on an input of size n. Similarly, an answer of n means that we expect it to take n times as long on an input of size 4n versus on an input of size n. he order of the algorithm tells us how we a) 2n (b) 2 (d) n! e) n (f) (Optional) log2 n