Chapter 1.1, Problem 13E

Round all answers to two decimal places unless otherwise indicated.

Note Some of the formulas below use the special number $e$, which was presented in the Prologue.

13. Radioactive Substances change form over time. For example, carbon 14, which is important for radiocarbon dating, changes through radiation into nitrogen. If we start with 5 grams of carbon 14, then the amount $C=C\left(t\right)$ of carbon 14 remaining after t years is given by

$C=5\times {0.5}^{t/5730}$

a. Express the amount of carbon 14 left after 800 years in functional notation, and then calculate its value.

b. How long will it take before half of the carbon 14 is gone? Explain how you got your answer. (Hint: You might use trial and error to solve this, or you might solve it by looking carefully at the exponent.).