When downloading a large file Travis noticed that the estima

When downloading a large file, Travis noticed that the estimated time remaining to complete the download decreased by 40 seconds for each additional megabyte downloaded. When he started the download there were 100 seconds remaining. Determine the constant rate of change, k, of the number of seconds remaining to complete the download with respect to the number of megabytes downloaded. Write a formula to determine the change in the number of seconds remaining to complete the download. delta t, in terms of the change in the number of megabytes downloaded, delta m. Write a formula to determine the number of seconds remaining to complete the download, t, in terms of the number of megabytes downloaded, m. Determine whether the following statement is always true, sometimes true or never true. If delta y = k delta x then y = kx?

Solution

At start of download , time remaining= 100s

After 1 mb download, time remaining =(100-40) s

After m mb download, time remaining , t = 100-40m

Constant rate of change, k= dt/dm= -40 s/mb

b) delta t = 100 - 40 delta m

c) t = 100-40m as determined above.

d) only vice versa is always true that is if y=kx

Then, delta y = k delta x