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:1) Calculate exponential decay by applying it

to the half life of an element

2) Write an exponential decay function given two consecutive data points.

DefinitionThe Exponential decay function has the form where 0 > |b| > 1

𝑓 (𝑥 )=2( 12 )𝑥

Example 1- Half LifeHalf-life is the amount of time it takes an element to decay. The equation for half-life is:

a = original amount t = time

During Chernobyl let’s say: 23.7 g of Pu-238 were released The half life of Pu-238 is 88 years 0.00000412 g is deadly to humans

It has been 30 years since Chernobyl, how much Pu-238 is left?

Step 1) Calculate the number of half-lives there were so far:

Step 2) Solve for amount using your answer from #1 as t:

is leftYou 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.

To write an exponential decay function:

1)Take the current amount and make that year zero to write the ordered pair (0, 28,600)

-Your original amount is a=28,600

2) Take the amount from the year before and write it as the ordered pair (-1,30,000) . Set the y-value from the previous year equal to and solve for b since you know a.

Solving, we get: b=0.953

3) Write your function:

So, after 30 years:

6748 Acres left after 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.

1)Write a function to model the population of the city

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

3)About when will the population hit 50,000 people?