Grade 12 Applied Math question

Question

Plutonium-239 is one of the most common isotopes used in nuclear power plants. If left in the environment, it decays naturally over time. The approximate time for plutonium-239 to decay is given by the function t = –80 390.66 log P where t is time in years and P is the percent of the original amount remaining, as a decimal.

a) Describe the location of any intercepts, the domain and range within the context of the question, and whether the function is increasing or decreasing.

b) How long, in years, will it take for 50% of the original amount to remain?

Answer 1

for b: one half life is defined as the time required for 50% of the radioactivity to remain.

-80390.66 log .5 = 24200 years.

We usually graph time as the domain and the amount remaining as the range.

The domain, time runs from 0 to infinity. The range runs from 1 (100%) and approaches 0.

HINT: if you are using Desmos or a graphing calculator, change the x axis only to 0 to 1 million. The Y axis should be 0-1 or 0-5. This isotope has a very long half life, so in many programs, the graph will look like a straight line. The function is a decreasing, concave upward curve with a limit of 0 at x = infinity.