1. Growth and Decay
Exponential Models

2. Exponential Growth Function
n(t)=n0 ekt, k>0 or
n(t)=n0 at, a>1 n0= initial amount=n(0)
a = growth factor
n(t)∞ as t∞

3. Exponential Decay Function
n(t)=n0 ekt, k<0 or
n(t)=n0 at, 0<a<1 n0= initial amount=n(0)
a = decay factor
n(t)0 as t∞

4. Compound Interest Compound interest is an exponential growth model
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 grows Carb decays
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