On March 11, 2011, Japan suffered an earthquake and tsunami thatcaused a disastrous accident at the Fukushima nuclear power plant.Among many other results, amounts of iodine-131 that were 27 timesthe government limit were found in a sample of spinach 60 milesaway.†Now, 27 times the government limit of iodine-131 is 54thousand becquerels per kilogram.†The following table shows theamount I, in thousands of becquerels per kilogram, ofiodine-131 that would remain after t days.
| t = time, in days | I = amount of
iodine-131 |
|---|
| 0 | 54.00 |
| 1 | 49.52 |
| 2 | 45.41 |
| 3 | 41.64 |
| 4 | 38.18 |
(a)
Show that the data are exponential. (In this part and the next,round to three decimal places.)
Because t increases by 1 each time, to show that thedata are exponential, we must show that the successive ratios(rounded to three decimal places) are the same. Because all of theratios are equal to  , the data are exponential.
(b)
Find an exponential model I that shows the amount ofiodine-131 present after t days.
I(t) =
(c)
How long will it take for the amount of iodine-131 to fall tothe government limit of 2 thousand becquerels per kilogram? Roundyour answer to the nearest whole day.
days
