Continuation of exponential modeling and applications. Continuation of exponential modeling and applications.

1. Exponential Modeling
Fossil 2

2. Exponential Modeling
The basic function:
How we model real life situations depends on what kind, or how much ,
information we are given:
Case 1: Working with a minimal amount of information (A,Ao, ∆t).
We will create a model in base 10 and base e ... base e is prefered.
is the original amount of quot;substancequot; at the
beginning of the time period.
A is the amount of quot;substancequot; as the end of the time
period.
Model is our model for the growth (or decay) of the
substancequot;, it is usually an exponential expression in
base 10 or base e although any base can be used.
t is the amount of time that has passed for the
substancequot; to grow(or Decay) from to A.

3. Example: The population of the earth was 5.3 billion in 1990. In 2000 it was
6.1 billion.
(a) Model the population growth using an exponential function.
(b) What was the population in 2008?
World Population Clock

5. (b) What will be the population in 2008?

6. Case 2: Given lots of information ( , m, p)
A is the amount of quot;substance quot; at the end of the time period.
is the original amount of quot;substancequot; at the beginning of
the time period.
m is the quot;multiplication factorquot;or growth rate.
p is the period; the amount of time required to multiply by
quot;mquot; once.
t is the time that has passed.

7. Example 1: A colony of bacteria doubles every 6 days. If there were 3000
bacteria to begin with how many bacteria will there be in 15 days?

8. The Troubles with Tribbles
Video Source

10. Example 2: The mass (in grams) of radioactive material in a sample is given by:
where t is measured in years.
(a) Find the half-life of this radioactive substance.
(b) Create a model using the half-life you found in (a). How much of a 10 gram
sample of the material will remain after 40 years?

12. Example 2: The mass (in grams) of radioactive material in a sample is given by:
where t is measured in years.
(b) Create a model using the half-life you found in (a). How much of a 10 gram
sample of the material will remain after 40 years?

14. A $5000 investment earns interest at the annual rate of 8.4% compounded monthly.
a) What is the investment worth after one year?
b) What is it worth after 10 years?
c) How much interest is earned in 10 years?