Unformatted text preview: Question 5
Your answer is CORRECT. A disease is spreading through a cit,3.r of population M (constant:lEtlppose 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 dig 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.
‘“ 701—? 2 Kim“ to)? A EDDgalon tank, tartally tilIl ofoi, develops a leak at the bottom LetA{r} be the autumn ofoil inthe tank
at line LEIJppose that the an'mn'n of oil is decreasing at a E Mutual to the square root of arnotmt of ﬂilpresemmtheban‘el] 0)
' ,— : “kl 24 siﬂmnaamﬂmmmmagnsﬂmmml sailInt J4; r13 Frlrnget ——— : .. /< /‘£ {a} Give the mummies nude] [mlvalue problem) a: . 5 ’4
(b)Findtlte general solution ofthe dismal equation as). Z [A ' ; __ [<16 4' C
{c} Find the partimhlr suhttbn lint satisﬁes the irlithlco .' ea
— if +J50' C) {401500 _
Question ll] W” C o A certain radioactive material, decaying at a » a
a halflife of 4 days. If a laboratory had an initial sample of lﬂﬂ grams of the material, t'md. , 14 1!,
{a} The amount Mt} present at any time t. ’4 : A 0 e
{b} The amount present aﬂer 6 days.
{c} The time required for the sample to lose sea of its mass. V K t
I (q U j l 0 ° 6,
lel .L . j i A
K
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l)\ ’__ lk ( 1:3 5“ 7. ”like ...
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 Fall '08
 morgan
 Math

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