Chapter 4.3, Problem 6E

Reminder Round all answers to two decimal places unless otherwise indicated.

The Fukushima Disaster 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.

$t=\text{time,}\text{in}\text{days}$	$I=\text{amount}\text{of}\text{iodine-131}$
$0$	$54.00$
$1$	$49.52$
$2$	$45.41$
$3$	$41.64$
$4$	$38.18$

a. Show that the data are exponential. (In this part and the next, round to three decimal places)

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

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.