Unformatted text preview: Question 5
Your answer is CORRECT. A disease is spreading through a city of population M (ooostant). Suppose that
the rate at which the disease is spreading at time t is proportional to product of the
number of people who don‘t have the disease and the square root of the number of
people who do. Let PH] be the number of people who have the disease at time t.
Give the mathematical model {differential equation} which describes the spread of the
disease. 1'11 A Sillglen tank, iiitiallyﬁill ofoi, develops a leak at the bottom Letsitfr} be the amount ofoil inthe tank
at line 1‘, Suppose ti'atthe amolintofoil is decreasingat arate proportionalto the sqtmre root ofamotmt of
oilpresent inthe barrel sMnaaMWWmﬂWUMﬂHIﬂmm I13 Prlrl Tart
{a} Gite the mathematical model (trialval]: problem) ﬁor A.
(h) Find the general sohiion of the diﬁrential eqmtion i1{a).
to} Find the partieuhr solution tint satisﬁes the initial eondiion. Question it] A certain radioactive material, decaying at a rate proportional to the amount present, has
a halfﬁfe of 4 days. If a laboratory had an initial sample of Int} grams of the material,
ﬁnd: {a} The amount Mt} present at any time t. {h} The amount present after t5 days. to} The time required for the sample to lose 911% of its mass. ...
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 Fall '08
 morgan
 Math

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