Exponential Growth and Decay 6.4. Exponential Decay Exponential Decay is very similar to Exponential Growth. The only difference in the model is that.

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Presentation transcript:

Exponential Growth and Decay 6.4

Exponential Decay Exponential Decay is very similar to Exponential Growth. The only difference in the model is that k is negative. Exponential Decay is very similar to Exponential Growth. The only difference in the model is that k is negative.

Half Life Half life is the amount of time it takes for a radioactive substance to decay to half of its original mass. To find a formula for half life we use our general equation for exponential decay. Half life is the amount of time it takes for a radioactive substance to decay to half of its original mass. To find a formula for half life we use our general equation for exponential decay.

Half Life

Example The half-life of radium 226 is 1590 years. A sample of radium 226 has a mass of 100 mg. Find a formula for the mass which remains after t years. The half-life of radium 226 is 1590 years. A sample of radium 226 has a mass of 100 mg. Find a formula for the mass which remains after t years.

Example Use the model that you just found to find the mass after 1000 years. Use the model that you just found to find the mass after 1000 years.

Example Use the same model to find when the mass will be reduced to 30 mg. Use the same model to find when the mass will be reduced to 30 mg.

Carbon Dating We use Carbon 14 which has a half life of about 5700 years to date objects. We use Carbon 14 which has a half life of about 5700 years to date objects.

Example It is found that 14% of the Carbon 14 originally present in an old simple tool has decayed. Find the approximate age of the tool. It is found that 14% of the Carbon 14 originally present in an old simple tool has decayed. Find the approximate age of the tool.

Homework Pg357 #21, 22, 25, 26, 35, 37, 40 Pg357 #21, 22, 25, 26, 35, 37, 40