Question

A researcher has funds to buy enough computing power to number-crunch a problem in 7 years. Computing power per dollar doubles every 17 months.

When should he buy his computers to have finished the problem as soon as possible? Give your answer as a decimal in months.

Suppose the problem would take C months on current computers. What is the largest value of C for which he should buy the computers immediately?

Answer 1

ist part answer :after 34 months(no. of months one is succesively saving by shifting the time should be greater than 17 months. For example if u by immediately time is 7 years bt if u buy after 17 month u save computing time3.5 yrs, so u save a net of 3.5yrs-17/12 yrs. As you can see the shift to next 17 months will save computing time to 3.5/2 =21 months so net saving of 4 months. Bt next shift will make computing time saved to be less than 17 months so will increase actual time. So the equation to look is when does (17/12)-(3.5/2^y) becomes negative for the first tym and then (y-1)*17 is the no. of months when you should buy)
second part:34 months

Answer 2

Sorry in above text please correct "when does (17/12)-(3.5/2^y) becomes negative for the first tym and then (y-1)*17 is the no. of months when you should buy"as
when does (17/12)-(7/2^y) becomes positive for the first tym and then (y-1)*17 is the no. of months when you should buy