Question

The intensity I of an x-ray after it has passed through a material that is x centimeters thick is given by I = I0e^–kx, where I0 is the initial intensity of the x-ray and k is a number that depends on the material. The constant k for copper is 3.2. Find the thickness of copper necessary so that the intensity of an x-ray after passing through the copper is 25% of the original intensity. Round to the nearest tenth.

Answer 1

.25 = e^-3.2x
so
ln .25 = -3.2 x

x = -ln .25/3.2