Algebra 2 Notes
April 30, 2009
1) The birth rate of a colony of ants is 60% per year.
The Death rate is 46%. Assume the starting
population is 650 ants.
◦ A) What is the difference between the birth and the death
rates?
◦ B) Is the population increasing or decreasing?
◦ C) Write an equation that could model this situation.
◦ D) Using this equation: how big will the colony be after 4
years?
2) Challenge: Write a story problem that could be
modeled with the equation y=20(1.1)^x

The half-life of a radio active substance is the time
it takes for half of the material to decay. A hospital
prepares a 100-mg supply of technetium-99m, which
has a half life of 6 hours.
◦ How much technetium-99m is left after 6 hours? After 12
hours? 18 hours?
◦ Write an exponential function to find the amount of
technetium-99m after x number of hours
◦ Use your equation to find the amount of material left after
75 hours.

Graph the equation from the last example in your
calculator
◦ Use the window
 -30<x<100, count by 10; -100<y<400, count by 40

What value does the graph seem to be approaching
but never cross?
◦ This is called an asymptote (pronounced: ass-im-tote…
excuse the foul language!)
◦ In particular this is a horizontal asymptote


Study this equation:
Use your previous knowledge about ‘a’, ‘h’ and ‘k’ to
make a conjecture about what they mean in terms of
the graph of this type equation (write them down
real quick!)
You were right!!!! 

‘a’ will stretch or shrink the graph

‘h’ will translate the graph horizontally (x-axis)
◦ (+ moves left, - moves right!)

‘k’ will translate the graph vertically (y-axis)
◦ In other words, ‘k’ moves the asymptote from 0 to k
The number …… e!!!



e represents the number 2.71828128…
e is used to represent continual growth or decay
(think ‘e’ for exponential growth and decay)
e is a number like pi
◦ It is an irrational number (it cannot be written as a
fraction)
Amount in Account
Rate of annual interest
Time in years
Principal (starting) Amount

Suppose you invest $1050 at an annual
interest rate of 5.5% compounded
continuously. How much money, to the
nearest dollar, will you have in the
account after 5 years?
P=
r=
t=
A=
what you’re solving for
 Suppose
you invest $1300 at an
annual interest rate of 4.3%
compounded continuously. Find the
amount you will have in the account
after 3 years.
◦ How much profit did you make in 3
years??
 Page
442 #15-17, 19, 21,
23, 24-26, 30, 32-36, 40,
41.