Growth and Decay

1
GrowthandDecay

• Exponential Models

2
Exponential Growth Function

• n(t)n0 ekt, kgt0
• or
• n(t)n0 at, agt1n0 initial amountn(0)
• a growth factor
• n(t)?8 as t?8

3
Exponential Decay Function

• n(t)n0 ekt, klt0
• or
• n(t)n0 at, 0ltalt1n0 initial amountn(0)
• a decay factor
• n(t)?0 as t?8

4
Compound Interest

• Compound interest is an exponential growth model
• A300(10.06)5
• Initial amount 300
• Growth Factor 1.06

5
Half Life

• Half Life is an exponential decay model
• A certain material has a half life of one year.
  If the initial mass is 50g,
• Find the mass as a function of time
• M(t)50(1/2)t
• Initial Amount 50
• Decay Factor 1/2

6
Half Life

• A radioactive element has half-life of 2.8 years.
  How long would it take 1 gram amount to decay to
  0.2 grams? Assuming exponential decay.

7
Half Life

• A radioactive element has half-life of 2.8 years.
  How long would it take 1 gram amount to decay to
  0.2 grams? Assuming exponential decay.

8
Half Life

• A type of chemical element has a half-life of 120
  years. In 2010, the amount of element is 10
  grams.
• In what year will the mass become 2.5 grams?
• 2 half-life periods needed
• t 240 years
• In what year will the mass become 1.5 grams?

9
Exponential Growth

• The population of a certain bacteria grows
  exponentially with time. It grows from 20 to 50
  in 13 hours. How much longer does it take to
  grow to 500?

10
Exponential Decay

• The face value of money depreciates by 4.5 each
  year. How long does depreciate to half of its
  original value?

11
Exponential Decay

• A certain type of material decays from 87 grams
  to 57 grams in 30 days. After how many more days
  will it decay to 27 grams? Assuming exponential
  decay.

12
Fashion growsCarb decays

• Fin