MATH 128 Baltimore City Community College Modeling Report

Please answer showing work and clearly showing answer , need detailed step by step solution to ensure comprehension

Question 1
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B0/1 pt 52 99 0 Details
You go to the doctor and he gives you 15 milligrams of
radioactive dye. After 20 minutes, 7.75 milligrams of dye
remain in your system. To leave the doctor’s office, you
must pass through a radiation detector without sounding the
alarm. If the detector will sound the alarm if more than 2
milligrams of the dye are in your system, how long will your
visit to the doctor take, assuming you were given the dye as
soon as you arrived? Give your answer to the nearest
minute.
minutes at the
You will spend
doctor’s office.
Question 7
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Question 6
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The doubling period of a bacterial population is 10 minutes.
At time t = 120 minutes, the bacterial population was 80000.
A bacteria culture initially contains 2500 bacteria and
doubles every half hour.
What was the initial population at time t = 0?
Find the size of the baterial population after 40 minutes.
Find the size of the bacterial population after 3 hours.
Find the size of the baterial population after 9 hours.
Question 4
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Question 5
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ū0/1 pt 52 99 0 Details
At the beginning of an experiment, a scientist has 352 grams
of radioactive goo. After 255 minutes, her sample has
decayed to 22 grams.
What is the half-life of the goo in minutes?
A wooden artifact from an ancient tomb contains 25 percent
of the carbon-14 that is present in living trees. How long
ago, to the nearest year, was the artifact made? (The half-
life of carbon-14 is 5730 years.)
Find a formula for G(t), the amount of goo remaining at
time t. G(t)
=
years.
How many grams of goo will remain after 5 minutes?
Question 3
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Question 2
د »
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The half-life of Palladium-100 is 4 days. After 20 days a
sample of Palladium-100 has been reduced to a mass of 1
mg.
The half-life of Radium-226 is 1590 years. If a sample
contains 200 mg, how many mg will remain after 1000
years?
What was the initial mass (in mg) of the sample?
mg
What is the mass 4 weeks after the start?
Question 13
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B0/1 pt 52 99 0 Details
Question 12
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ū0/1 pt 52 99 0 Detail:
One earthquake has MMS magnitude 3.6. If a second
earthquake has 770 times as much energy (earth movement)
as the first, find the magnitude of the second quake.
The 1906 San Francisco earthquake had a magnitude of 7.9
on the MMS scale. Around the same time there was an
earthquake in South America with magnitude 3.9 that
caused only minor damage. How many times more intense
was the earth movement in San Francisco earthquake than
the South American one?
Question 10
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Question 11
V
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B0/1 pt 52 99 Detail
The number line below shows a value on a log scale.
A roasted turkey is taken from an oven when its
temperature has reached 185 Fahrenheit and is placed on a
table in a room where the temperature is 75 Fahrenheit.
Give answers accurate to at least 2 decimal places.
+
+
+
-5 -4 -3 -2 -1
log(x)
+
3 4 5
+
2
0
1
(a) If the temperature of the turkey is 153 Fahrenheit after
half an hour, what is its temperature after 45 minutes?
Fahrenheit
What is the value of the point?
X =
(b) When will the turkey cool to 100 Fahrenheit?
hours.
Question 8
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G0/1 pt 299 Details
The count in a bacteria culture was 900 after 10 minutes
and 1700 after 30 minutes. Assuming the count grows
exponentially,
Question 9
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ū0/1 pt 52 99 0 Detail
What was the initial size of the culture?
Find the time required for an investment of 5000 dollars to
grow to 7200 dollars at an interest rate of 7.5 percent per
year, compounded quarterly.
Your answer is t =
years.
Find the doubling period.
Find the population after 120 minutes.
II
When will the population reach 10000.