differential equations: two models for tank leakage

[carlasader]

A cylindrical tank with an horizontal circular base is leaking. At time "t" minutes, the depth of oil in the tank is "h" meters. It is known that h = 10 when t = 10, and that h = 5 when t = 40.

a) Alan assumes that the rate of change of h with respect to t is constant. Under his assumption, find an expression for h in terms of t.

b) Bhavana assumes that the rate of change of h with respect to t is proportional to h. Under her assumption, find an expression for h in terms of t.

c) Find, in each case, the value of h when t = 60.

d) Briefly explain which assumption you would use.

please try to help me solve it
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Edited by stapel -- Reason for edit: Replacing scan of text with actual text.

 

[skeeter]

Re: differential equations

a. rate of change of h w/r to t is constant ...

dh/dt = k

separate variables and integrate ... you have two data points, so you will be able to find the constant of proportionality and the constant of integration.

b. rate of change of h w/r to t is proportional to h ...

dh/dt = kh

same drill as above.

c. use your solutions from parts (a) and (b) to answer this question.

d. ... depends on what you know about fluid dynamics.

 

[stapel]

Various other posts of this exercise deleted.

please try to help me solve it

Please reply to this thread, showing how you've used the help you've already been provided, rather than reposting again.

Thank you.

Eliz.