Transcript 6.7 - People Server at UNCW

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
uo : 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?
500
Graph the function using a graphing utility.
What was the initial amount of bacteria?
grams.
When will the amount of bacteria be 300 grams?
days.