Exponential decay

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Warm Up Google “Chernobyl Disaster” to learn about what it was and identify some key points that you learn.
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Warm UpGoogle Chernobyl Disaster to learn about what it was and identify some key points that you learn.

The byproduct of nuclear power are the radioactive isotopes that get produced.

If not properly contained, exposure to these isotopes produces unwanted effects to the body(depending n how much exposure and for how long.

Even though there was a couple of isotopes in the Chernobyl disaster, to keep things simple we will focus on Plutonium 238 (PU-238)

Exponential DecayObjective:Calculate exponential decay by applying it to the half life of an element

Write an exponential decay function given two consecutive data points.

Definition

Example 1- Half Life

You try:

Will the immediate area around Chernobyl be safe in 10,000 year? Show calculation to justify your answer.

Example 2An explosion releases 2 grams of Cesium-137 (another harmful isotope) with a half life of 30 years. How much Cesium-137 will be left after 50 year?

Writing Exponential Decay FunctionsSuppose the rainforest is getting cut down at an exponential rate in a certain country.

There were 30,000 acres of rain forest last year. Now there are 28,600 acres left.

1) Write an exponential decay function to model the amount of rainforest

2) Use your function to find out how much acres will be left in 30 years.

Example 3The population of a city is shrinking exponentially. Last year the population was 200,000 people. This year there are 194,750 people left.

Write a function to model the population of the city

Use your function to calculate how much people will be left in 20 years

About when will the population hit 50,000 people?