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### Course: Algebra (all content)>Unit 11

Lesson 19: Constructing exponential models according to rate of change (Algebra 2 level)

# Constructing exponential models (old example)

Sal constructs a function to model the decay of a radioactive element. Created by Sal Khan.

## Want to join the conversation?

• Isn't the radiological half-life of Cesium-137 approximately 30 years, not 30 days?
• if after every 30 days the cesium-137 has half of what it had before, then it would go on infinitely because it just keeps on halving itself? I think it keeps getting closer and closer to 0 like an asymptote right?
• Theoretically yes, but cesium has a finite subdivision, meaning unlike pure numbers which are split into infinitesimals, cesium is split into a finite integer number of particles. And either way, once a radioactive element reaches a stable element isotope, it will stop decaying.
Nice question though.
• Is there something named after Marie Curie except for the element? Like is there a unit called the Curium that measures something like the Becquerel?
• A Becquerel is only 1 nucleus (decayed) per second. A Curie (originally the radiation from a gram of radium) is now 3.7 *10^10 nuclei per second.
(1 vote)
• how much is a becquerel?
• A becquerel (Bq) is a measure of how radioactive something is. It tells you the number of disintegrations per second.
• at sal says that the half life of cesium 137 is 30 years and the weight changes from 2kg to 1kg. so at the end of the half life period there will be only half of the elements mass left, right?!
thanks.
• Yes, but please understand that the mass just doesn't disappear. The cesium-137 turns into barium-137. So the half of the mass of cesium that decayed didn't just disappear, it merely changed into a different element. However, there is a small amount of matter-energy conversion involved.
• It can be annoyingly difficult reconciling exponential growth / decay problems done with Algebra 2 methodology with those done with differential equations. Are there videos comparing the two methods?
• how am i supposed to write 5^sqrt(0.5)? on the calculator?
• In the radioactive decay series, the equation was A(t) = A(0) * e^-lambda*t. This example confuses me.