3-28 exponential growth, decay, half-life, and compound
TRANSCRIPT
3-28 Exponential Growth and Decay, Half-Life, and Compound Interest.notebookMarch 28, 2014
Math Origami
How many times can you fold the piece of
paper?
Take a sheet a paper that is .001 cm thick.
3-28 Exponential Growth and Decay, Half-Life, and Compound Interest.notebookMarch 28, 2014
How thick is the paper after....
1 fold?
2 folds?
3 folds?
http://www.youtube.com/watch?v=AmFMJC45f1Q
3-28 Exponential Growth and Decay, Half-Life, and Compound Interest.notebookMarch 28, 2014
3-28 Exponential Growth and Decay, Half-Life, and Compound Interest.notebookMarch 28, 2014
Increasing exponentially means that the number
is constantly multiplying by itself.
Exponential growth can be modeled with the
function
OR
3-28 Exponential Growth and Decay, Half-Life, and Compound Interest.notebookMarch 28, 2014
Ex. 1) Identify the initial amount a and the
growth factor b in each exponential function.
a.)
b.)
3-28 Exponential Growth and Decay, Half-Life, and Compound Interest.notebookMarch 28, 2014
Ex. 2) Since 1985, the daily cost of patient care in
community hospitals in the US about 8.1% per year.
In 1985, such hospital costs were an average of $480
per day.
a.) Write an equation to model the cost of hospital care.
b.) Use your equation to find the approximate cost per day
in 2000?
3-28 Exponential Growth and Decay, Half-Life, and Compound Interest.notebookMarch 28, 2014
Decreasing exponentially means that the number is
constantly dividing by itself.
Exponential decay can be modeled by the function
3-28 Exponential Growth and Decay, Half-Life, and Compound Interest.notebookMarch 28, 2014
Ex. 3) Since 1980, the number of gallons of whole
milk each person in the US drinks each year has
decreased 4.1% each year. In 1980, each person
drank an average of 16.5 hallons of whole milk per
year.
a.) Write an equation to model the gallons of whole
milk drunk by one person.
b.) Use your equation to find the approximate
consumption per person of whole milk in 2000.
3-28 Exponential Growth and Decay, Half-Life, and Compound Interest.notebookMarch 28, 2014
Compound Interest
When the bank pays interest on both the initial
amount and the interest the account has already
earned.
3-28 Exponential Growth and Decay, Half-Life, and Compound Interest.notebookMarch 28, 2014
Ex. 3) Suppose your parents deposited $1500 in an
account paying 6.5% interest compounded annually
when you were born. Find the account balance after
18 years.
3-28 Exponential Growth and Decay, Half-Life, and Compound Interest.notebookMarch 28, 2014
Ex. 4) Find the balance in the account.
$4000 principal earning, 6% compounded annually,
after 5 years
3-28 Exponential Growth and Decay, Half-Life, and Compound Interest.notebookMarch 28, 2014
Half-Life
Over x (days, months, years, etc.) the amount of
substance is divided in half.
Ex. 5) The half-life of iodine-124 is 4 days. A
technician measures a 40-mCi sample of iodine-124.
a.) How many half-lives of iodine-124 occur in 16
days?
b.) How much iodine-124 is in the sample 16 days
after the technician measures the original sample?
3-28 Exponential Growth and Decay, Half-Life, and Compound Interest.notebookMarch 28, 2014
Homework
Page 441 Exercises 1-8,12-18
3-28 Exponential Growth and Decay, Half-Life, and Compound Interest.notebookMarch 28, 2014