Exponential Growth and Decay, and Newtons Law of Cooling Story Problems

1
Exponential Growth and Decay, and Newtons Law of
Cooling Story Problems

• 4.8

2
Uninhibited Growth and Decay Formula

• A Ao ekt
• If kgt0, then uninhibited growth
• If klt0, then uninhibited decay

3
Half-Life

• The time required for half of a radioactive
  substance to decay.

4
Carbon Dating

• Dating an organism using carbon properties.
• All organisms contain carbon 12, a stable carbon,
  and carbon 14, a radioactive carbon with a
  half-life of 5600 years.
• When an organism dies, the carbon 12 stays the
  same, but the carbon 14 begins to decay.

5
Newtons Law of Cooling

• u(t) T (uo T)ekt
• T is the temperature of the surrounding medium
• uo is the initial temperature
• k is a negative constant--rate

6
Exponential Growth Example

• 2 from the text

7
Exponential Decay Example

• 4 from the text

8
Exponential Solving Example

• 8,10,12 from the text

9
Newtons Law of Cooling Example

• 14 from the text

10
Logistic Example

• 24 from the text