Chapter 1.2, Problem 13E

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

t is measured in thousands of years, and $C=C\left(t\right)$ is the amount, in grams, of carbon-14 remaining.

Carbon-14

unstable (radioactive)

$\begin{array}{c}t=\text{Thousand}\\ \text{of}\text{years}\end{array}$	$C=\text{Grams}\text{remaining}$
$0$	$5$
$5$	$2.73$
$10$	$1.49$
$15$	$0.81$
$20$	$0.44$

a. What is the average yearly rate of change of carbon-14 during the first 5000 years?

b. How many grams of carbon-14 would you expect to find remaining after 1236 years?

c. What would you expect to be the limiting value of C?