Chapter 4.3, Problem 14E

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

The half life of ${}^{239}U$ Uranium-239 is an unstable isotope of uranium that decays rapidly. In order to determine the rate of decay, 1 gram of ${}^{239}U$ was placed in a container, and the amount remaining was measured at 1-minute intervals and recorded in the table below.

Time, in minutes	Grams remaining
$0$	$1$
$1$	$0.971$
$2$	$0.943$
$3$	$0.916$
$4$	$0.889$
$5$	$0.863$

a. Show that these are exponential data and find an exponential model (For this problem, round all your answers to three decimal places.)

b. What is the percentage decay rate each minute? What does this number mean in practical terms?

c. Use functional notation to express the amount remaining after 10 minutes and then calculate the value.

d. What is the half life of ${}^{\text{239}}\text{U}$?