A student is trying to determine the half-life of radioactive iodine-131. They measure the amount, I, of iodine-131 in a sample solution every 8 hours. Their data are shown in the table. Time (hours) Amount (grams) 8 4.88 16 4.71 24 4.60 32 4.48 40 4.39 48 4.28 a. Find a fully defined exponential model of the data. (Round all numerical values to three decimal places.) E(t) = t 4. ≤48 grams is the amount of iodine-131 in a sample solution after thours where 8 9. b. Find a fully defined logarithmic model of the data. (Round all numerical values to three decimal places.) is the amount of iodine-131 in a sample solution after thours L(t) = 2. grams t 948 2. where 8 c. Use the unrounded models in Parts a and b to estimate the amount of iodine-131 after 29 hours. (Round your answers to three decimal places.) E(29)= grams L(29) = grams d. Which of the two models better displays the end behavior suggested by the context? The exponential model.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter14: Data Mining
Section14.2: Classification Methods
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A student is trying to determine the half-life of radioactive iodine-131. They measure the amount, I, of iodine-131 in a sample solution every 8 hours. Their
data are shown in the table.
Time (hours) Amount (grams)
8
4.88
16
4.71
24
4.60
32
4.48
40
4.39
48
4.28
a. Find a fully defined exponential model of the data. (Round all numerical values to three decimal places.)
E(t) =
t
4.
≤48
grams
is the amount of iodine-131 in a sample solution after thours
where 8
9.
b. Find a fully defined logarithmic model of the data. (Round all numerical values to three decimal places.)
is the amount of iodine-131 in a sample solution after thours
L(t) =
2.
grams
t
948
2.
where 8
c. Use the unrounded models in Parts a and b to estimate the amount of iodine-131 after 29 hours. (Round your answers to three decimal places.)
E(29)=
grams
L(29) =
grams
d. Which of the two models better displays the end behavior suggested by the context? The exponential model.
Transcribed Image Text:A student is trying to determine the half-life of radioactive iodine-131. They measure the amount, I, of iodine-131 in a sample solution every 8 hours. Their data are shown in the table. Time (hours) Amount (grams) 8 4.88 16 4.71 24 4.60 32 4.48 40 4.39 48 4.28 a. Find a fully defined exponential model of the data. (Round all numerical values to three decimal places.) E(t) = t 4. ≤48 grams is the amount of iodine-131 in a sample solution after thours where 8 9. b. Find a fully defined logarithmic model of the data. (Round all numerical values to three decimal places.) is the amount of iodine-131 in a sample solution after thours L(t) = 2. grams t 948 2. where 8 c. Use the unrounded models in Parts a and b to estimate the amount of iodine-131 after 29 hours. (Round your answers to three decimal places.) E(29)= grams L(29) = grams d. Which of the two models better displays the end behavior suggested by the context? The exponential model.
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