Question

On March 11, 2011, Japan suffered an earthquake and tsunami that caused a disastrous accident at the Fukushima nuclear power plant. Among many other results, amounts of iodine-131 that were 27 times the government limit were found in a sample of spinach 60 miles away.† Now, 27 times the government limit of iodine-131 is 54 thousand becquerels per kilogram.† The following table shows the amount I, in thousands of becquerels per kilogram, of iodine-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 the data are exponential, we must show that the successive ratios (rounded to three decimal places) are the same. Because all of the ratios are equal to  , the data are exponential.

(b)

Find an exponential model I that shows the amount of iodine-131 present after t days.

I(t) =

(c)

How long will it take for the amount of iodine-131 to fall to the government limit of 2 thousand becquerels per kilogram? Round your answer to the nearest whole day.

days

Answer 1

On March 11, 2011, Japan suffered an earthquake and tsunami that caused a disastrous accident at the Fukushima nuclear power plant. Among many other results, amounts of iodine-131 that were 27 times the government limit were found in a sample of spinach 60 miles away.