Iodine 131 is a radioactive isotope that decays as time passes. The function M(t) = 200e-0.093t...

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Iodine 131 is a radioactive isotope that decays as time passes.The function M(t) = 200e^-0.093t gives the mass of Iodine131 remaining in the sample measured in grams in terms oft number of days since the samples mass was originallymeasured.
a) What was the initial mass of Iodine 131?
b) What is the one days decay factor and what is the one daypercent change?
c) How long will it take for the sample to decay such that onlyhalf of the original mass of Iodine 131 still remains?
d) How long will it take for only 35 grams of Iodine 131 tostill be present in the sample?
e) What is the mass of the remaining Iodine 131 after one weekhas passed since the mass was originally measured?
f) What is the one week growth factor, and what is the one weekpercent change?
g) Write a function B that closely approximates themass of the remaining Iodine 131 in the samplemeasured in grams interms of the number of weeks w since the samples mass wasoriginally measured?
h) What is the one hour growth factor, and what is the one hourpercent change?
g) Write a function C that closely approximates themass of the remaining Iodine 131 in the sample measured in grams interms of the number of hours h since the samples mass wasoriginally measured?

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3.7 Ratings (310 Votes)

a When t 0 we have M0 200 so the mass of Iodine 131 was 200 grams b When t 0 M1 200e0093 Hence one days decay factor is 0093 Also M1 200e0093 20009111935 182239 grams on rounding off to the nearest milligram Thus the one day change is 200182239200100 888 on rounding off to 2 decimal places c Let the sample take t days to decay such that only half of the original mass of Iodine 131 still remains Then 100 See Answer

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