Can someone please help me with the differential equation question!!!?

blue01

2011-04-20 6:02 am

ITS manage centralized data storage across the university. In their provisioning for growth in the system they model the typical user’s data requirements to grow at a rate proportional to the square root of their current disk usage. To limit the size of the system each user is allocated a maximum of 2 Gb storage. Due to this they assume that users delete obsolete files at a rate inversely proportional to the size of their remaining disk space. Write down a differential equation to describe the change in a user’s disk storage each day. State clearly what each variable/symbol means in your DE (there should be 4 symbols in the DE).

回答 (1)

[匿名]

2011-04-21 8:43 am

✔ 最佳答案

Let S(t) be the space taken up by a user's data at time t.

You are told that the user's space requirements increase at a rate proportional to sqrt(S), so:

rate space use increases = a*sqrt(S)

where a is a positive constant of proportionality.

At time t, a user's remaining space is given by (2 - S), where S is measured in Gb. You are told that the user frees up disk space at a rate inversely proportional to the remaining space, so:

rate space use decreases = -b/(2 - S)

where b is another positive constant of proportionality.

The net rate of chance in disk space usage is the sum of these two rates:

dS/dt = a*sqrt(S) - b/(S-2)

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