Worksheet 5.1 - Separable Differential Equations With Answers - Calculus Maximus

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Calculus Maximus
WS 5.1: Separable Diff EQ
Name_________________________________________ Date________________________ Period______
Worksheet 5.1—Separable Differential Equations
Show all work. No Calculator unless specified.
Multiple Choice
1. (Calculator Permitted) A sample of Kk-1234 (an isotope of Kulmakorpium) loses 99% of its
radioactive matter in 199 hours. What is the half-life of Kk-1234?
(A) 4 hours
(B) 6 hours
(C) 30 hours
(D) 100.5 hours
(E) 143 hours
dy
2. In which of the following models is
directly proportional to y?
dt
kt
I.
y
e
C
kt
II.
y
Ce
kt
III.
y
28
3 1
t
1
IV.
y
3
2
(A) I only (B) II only (C) I and II only
(D) II and III only (E) II, III, and IV (F) all of them
3. (Use your calculator on this one, but get the exact answer first.) The rate at which acreage is being
consumed by a plot of kudzu is proportional to the number of acres already consumed at time t. If there
are 2 acres consumed when
t
1
and 3 acres consumed when
t
5
, how many acres will be consumed
when
t
8
?
(A) 3.750
(B) 4.000
(C) 4.066
(D) 4.132
(E) 4.600
4. (‘88-BC43) Bacteria in a certain culture increase at a rate proportional to the number present. If the
number of bacteria doubles in three hours, in how many hours will the number of bacteria triple?
æ
ö
æ
ö
3ln 3
2ln3
ln 3
27
9
(A)
(B)
(C)
(D) ln
(E) ln
è ç
ø ÷
è ç
ø ÷
ln 2
ln 2
ln 2
2
2
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