Economics Dynamics Problems 65

Economics Dynamics Problems 65 - Continuous dynamic systems...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Continuous dynamic systems 49 Figure 2.11. Example 2.14 Testing for art forgeries 5 All paintings contain small amounts of the radioactive element lead-210 and a smaller amount of radium-226. These elements are contained in white lead which is a pigment used by artists. Because of the smelting process from which the pigment comes, lead-210 gets transferred to the pigment. On the other hand, over 90 per cent of the radium is removed. The result of the smelting process is that lead-210 loses its radioactivity very rapidly, having a half-life of about 22 years; radium-226 on the other hand has a half-life of 1,600 years (see example 2.7). For most practical purposes we can treat radium-226 emissions as constant. Let l ( t ) denote the amount of lead-210 per gram of white lead at time t , and l 0 the amount present at the time of manufacture, which we take to be
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online