A patient undergoing a heart scan is given a sample of fluorine- 18 1 8 F . After 4 hr , the radioactivity level in the patient is 44.1 MBq (megabecquerel). After 5 hr, the radioactivity level drops to 30.2 MBq . The radioactivity level Q t can be approximated by Q t = Q 0 e − k t , where t is the time in hours after the initial dose Q 0 is administered. a. Determine the value of k . Round to 4 decimal places. b. Determine the initial dose, Q 0 . Round to the nearest whole unit. c. Determine the radioactivity level after 12 hr . Round to 1 decimal place.
A patient undergoing a heart scan is given a sample of fluorine- 18 1 8 F . After 4 hr , the radioactivity level in the patient is 44.1 MBq (megabecquerel). After 5 hr, the radioactivity level drops to 30.2 MBq . The radioactivity level Q t can be approximated by Q t = Q 0 e − k t , where t is the time in hours after the initial dose Q 0 is administered. a. Determine the value of k . Round to 4 decimal places. b. Determine the initial dose, Q 0 . Round to the nearest whole unit. c. Determine the radioactivity level after 12 hr . Round to 1 decimal place.
Solution Summary: The author calculates the value of k and round off to 4 decimal places for the following model in which the radioactivity level Q(t) can be approximated.
A patient undergoing a heart scan is given a sample of fluorine-
18
1
8
F
.
After
4
hr
, the radioactivity level in the patient is
44.1
MBq
(megabecquerel). After
5
hr,
the radioactivity level drops to
30.2
MBq
.
The radioactivity level
Q
t
can be approximated by
Q
t
=
Q
0
e
−
k
t
,
where
t
is the time in hours after the initial dose
Q
0
is administered.
a. Determine the value of
k
. Round to
4
decimal places.
b. Determine the initial dose,
Q
0
. Round to the nearest whole unit.
c. Determine the radioactivity level after
12
hr
.
Round to
1
decimal place.
A tank contains 1000 liters (L) of a solution consisting of 154 kg of salt dissolved in water . Pure water is pumped into the tank at the rate of 3 L/s , and the mixture - kept uniform by stirring - is pumped out at the same rate . How long will it be until only 14 kg of salt remains in the tank ?
It will take about _____ seconds.
A 88.3 g piece of copper (specific heat 0.380 J/g.°C) is heated and
then placed into 400.0 g of water initially at 20.7°C. The water
increases in temperature to 22.2°C. What is the initial temperature (in
°C) of the copper? (The specific heat of water is 4.184 J/g °C).
Sulfur compounds cause “off-odors” in wine, so winemakers want to know the odor threshold, the lowest concentration of a compound that the human nose can detect. The odor threshold for dimethyl sulfide (DMS) in trained wine tasters is about 25 micrograms per liter of wine (μg/l). The untrained noses of consumers may be less sensitive, however. Here are the DMS odor thresholds for 10 untrained students:
31 31 43 36 23 34 32 30 20 24
Give a 95% confidence interval for the mean DMS odor threshold among all students.
Is there evidence that the mean threshold for untrained tasters is greater than 25 μg/l? State the hypotheses.
Is there evidence that the mean threshold for untrained tasters is greater than 25 μg/l? What is the test statistic?
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