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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 Sill-glen 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 sMnaaMWWmﬂWUMﬂH-Iﬂmm I13 Prlrl Tart {a} Gite the mathematical model (trial-val]: 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 half-ﬁfe 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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