1. 3.1 Growth and Decay

2. Uninhibited Growth of Cells
N0 is the initial population
k is the constant of growth
t is the time for the growth to the new population, N(t).

3. A colony of bacteria grows according to the law of uninhibited growth
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?

5. Uninhibited Radioactive Decay
A0 is the initial amount
k is the constant of decay
t is the time for the decay to the new amount, A(t).

6. The half-life of Uranium-234 is 200,000 years
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.

7. grams.

8. Newton’s Law of Cooling
T : Temperature of surrounding medium
uo : Initial temperature of object
k : A negative constant

9. A cup of hot chocolate is 100 degrees Celsius
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?

10. It will be 60 degrees in:
minutes.

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

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

14. 500 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.

15. What was the initial amount of bacteria?
grams.

16. When will the amount of bacteria be 300 grams?

17. days.