1) Derive a rule of thumb that applies with the runtime is proportional to sqrt(n)(log(n)), where n is the input size. The rule should apply when the input size is cubed. Make sure so show the math and eventually translate into a sentence of the form "When we cube the input size.... Do not use "n" in your sentence. Say "the original input size". 2) Suppose a program takes time proportional to sqrt(n)(log(n)), where n is the input size. If the program takes 10 ms to process input of size 100, how long will it take to process.... a) input if size 10,000. b) input of size 100,000,000.