6.7 Growth and Decay. Uninhibited Growth of Cells.

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Presentation transcript:

6.7 Growth and Decay

Uninhibited Growth of Cells

A colony of bacteria grows according to the law of uninhibited growth. If 100 grams of bacteria are present initially, and 250 grams are present after two hours, how many will be present after 4 hours?

Uninhibited Radioactive Decay

The half-life of Uranium-234 is 200,000 years. If 50 grams of Uranium-234 are present now, how much will be present in 1000 years. NOTE: The half-life is the time required for half of radioactive substance to decay.

grams.

Newton’s Law of Cooling T : Temperature of surrounding medium u o : Initial temperature of object k : A negative constant

A cup of hot chocolate is 100 degrees Celsius. It is allowed to cool in a room whose air temperature is 21 degrees Celsius. If the temperature of the hot chocolate is 80 degrees Celsius after 5 minutes, when will its temperature be 60 degrees Celsius?

It will be 60 degrees in: minutes.

Graph What happens to the value of u(t) as t increases without bound? The value of u(t) approaches 21.

Logistic Growth Model where a, b, and c are constants with c > 0 and b > 0.

The logistic growth model represents the amount of bacteria (in grams) after t days. What is the carrying capacity? Graph the function using a graphing utility. 500

What was the initial amount of bacteria? grams.

When will the amount of bacteria be 300 grams?

days.