# Chapter 7 - Section 7.2 - Exponential Change and Separable Differential Equations - Exercises - Page 411: 45

The fossil $6658.3$ years old.

#### Work Step by Step

The half life for carbon is 5700 years. Radioactive decay formula is: $y_0e^{-kt}=0$ This implies that $k=\dfrac{\ln 2}{5700}$ $e^{-\dfrac{\ln 2}{5700}t}=0.445$ Thus, $-\dfrac{\ln 2}{5700} t=\ln (0.445)$ so, $t=6658.3~years$

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