# Exponential Functions: basic form If b &gt; 1 then....

```Exponential Functions:
basic form y = a(b)x.
If b &gt; 1 then....
y -intercept
If b &lt; 1 then ...
Since 2004 your \$240,000 house has depreciated in value 6% a year.
you have to think of 'b' has 'how much is LEFT each year'
year.
In this case there is 94% of your house's value LEFT each
asymptote: either horizontal or vertical lines upon which your
function shall not pass. They are like walls that lets nothing
through.
If you have f(x) = 2
x-5
you can plug in any x value you want
other than 5, so you have an asymptote
at x= 5.
If you have f(x) = 2
x-5
you can plug in any x value you want
other than 5, so you have an asymptote
at x= 5.
Now, there are 50 bacteria in a dish which are growing
exponentially at a rate of 4.7%
a) Equation for this
b) What is the y-intercept
c) why is it wrong to plug in either .953 or 0.047 for b?
y = 50( 1 + 0.047 )x
Now, what is the asymptote for this graph?
Compare these two expo functions.
What are the respective y intercepts?
What conclusions can you
make about a graph if the a
value is negative?
Half Life Problems:
Say you have 100 grams of kyrponite. If we say
&quot;kyrponite has a half life of 5 years&quot; that means every 5
years HALF of the substance decays.
YEARS
0
5
10
15
GRAMS LEFT
100
50
25
12.5
What is your initial amount, a?
Now, what is your decay rate, b?
(Similar to the basketball tourney problem)
Now, how do you relate the half life
number in there?
25 years is how many half lives?
42 years is how many half lives?
half life formula:
y = ab
if something has a half life of 7 days and you
want to know how much is left after 80 days,
you are finding 80/7 or 11.43 half lives.
Homework to do:
pg. 442 #15-17, 19, 21, 23, 24-28, 30, 36, 37, 40, 41.
```