Question

Let b(t) represent the population of bunnies on Greentree Island t weeks after the population was first recorded.

Assume that b(0) =

126126,

b(20) =

12671267,

b(40) = 13571357

Integral from 10 to 20 b prime left parenthesis t right parenthesis dt∫1020b′(t)dt

=

475475,

Integral from 20 to 30 b prime left parenthesis t right parenthesis dt∫2030b′(t)dt

= 890890

A) What was the population on the island exactly 10 weeks after the population was first recorded?

B)

Integral from 0 to 10 b prime left parenthesis t right parenthesis dt∫010b′(t)dt

=

C) What was the population on the island exactly 30 weeks after the population was first recorded?

D)

Integral from 30 to 40 b prime left parenthesis t right parenthesis dt∫3040b′(t)dt

=

Answer #1

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ONLY EXERCISE B!
Find the mass that remains after t years.
Step 1
Let y(t) be the mass (in mg) remaining after
t years.
Then we know the following.
y(t)
=
y(0)ekt
=
10
10
· ekt
Step 2
Since the half-life is 30 years, then y(30) =
5
5
mg.
Step 3
Thus, 5 = 10e30k, or
e30k = 1/2
1/2
.
Therefore, k =
$$−ln(2)30
.
Step 4
Now, remembering that
ln(xn) =
n ln(x)
and that
eln(z)...

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One season, some individuals from the island migrate to the
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allele q in the mainland population in the next generation?
a) 0.4
b) 0.5
c) 0.1
d) 0
e) 0.6

Let P(t) represent the number of people who have been infected
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(a) Suppose P' (34) = 11. What does this tell us about the
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(b) Suppose that P' (58) = 0. Based on this information, do we
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(c) Suppose P'' (34) = 8. Based on this and on...

Suppose that the population develops according to the logistic
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What is the P value after 10 days where A = (M-P(0)) / P(0)) if the
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2.) After a boating mishap you find yourself stranded on a
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pairs of shoes in the crate. You manage to grab 10 left shoes and 5
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A) Suppose your pirate friend has only one good leg – his right
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2.) After a boating mishap you find yourself stranded on a
deserted island with a pirate and a crate of shoes. There are ten
pairs of shoes in the crate. You manage to grab 10 left shoes and 5
right shoes before being chased away by “Captain Hook.”
A) Suppose your pirate friend has only one good leg – his right
leg (his left leg is a wooden stump). Luckily, your feet are
intact. Let X1 denote right shoes and...

After a boating mishap, you find yourself stranded on a deserted
island with a pirate and a crate of shoes. There are ten pairs of
shoes in the crate. You manage to grab 10 left shoes and 5 right
shoes before being chased away by “Captain Hook”.
(a) Suppose your pirate friend has only one good leg – his right
leg (his left leg is a wooden stump). Luckily, your feet are
intact. Let x1 denote right shoes and x2...

Construct a scatterplot and identify the mathematical model that
best fits the data shown below. Let x represent the year since
1959, with 1960 coded as
xequals=1,
1973 coded as
xequals=14,
1986 coded as
xequals=27,
and so on. Let y represent the subway fare.
Year
1960
1973
1986
1995
2002
2003
Subway Fare
0.150.15
0.350.35
0.900.90
1.351.35
1.501.50
1.951.95
Choose the correct graph below.
A.
05003xy
A scatterplot has a horizontal x-scale from 0 to 50 in intervals
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9. Let t correspond to the number of months after January 15
with 0 ≤ t ≤ 12. A mathematical model for the variation of the
expected temperature during the year is given by T(t) = 20 − 2t(t −
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for the whole year in degrees Fahrenheit? (a) 70°F (b) 66°F (c)
68°F (d) 72°F (e) None of the above.
10. Carbon 14 (C-14), a radioactive isotope of carbon, has...

The members of a population have been numbered 1-50. A
sample of size 20 is to be taken from the population, using
cluster sampling. The clusters are of equal size 10, where
cluster #1 consists of the members of the population numbered
1dash10, cluster #2 consists of the members of the population
numbered 11-20, and so forth.
a. What are the clusters taken from the population?
b. Suppose that clusters #1 and #3 are selected from the clusters
determined in...

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