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Today’s Agenda
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Section 4.1
MyLabsPlus Homework due Sun.
E.C. Quiz Monday
Payday!You just got a job! You will work for 30 days. You may choose between three pay rates.
Rate Plan A pays $200,000 a day.
Rate Plan B pays $50,000 your first day and provides you with a $10,000 raise each subsequent day. (For instance, you earn $60,000 on the second day, $70,000 the third day, and so forth.)
Rate Plan C pays 2 cents the first day and doubles every subsequent day. (For instance, you earn 4 cents on the second day, 8 cents on the third day, and so forth)
Payday!Rate Plan B pays $50,000 your first day and provides you with a
$10,000 raise each subsequent day. (For instance, you earn $60,000
on the second day, $70,000 the third day, and so forth.)
Payday!Rate Plan C pays 2 cents the first day and doubles every
subsequent day. (For instance, you earn 4 cents on the second day,
8 cents on the third day, and so forth)
Payday!Rate Plan C pays 2 cents the first day and doubles every
subsequent day. (For instance, you earn 4 cents on the second day,
8 cents on the third day, and so forth)
Payday!Rate Plan C pays 2 cents the first day and doubles every
subsequent day. (For instance, you earn 4 cents on the second day,
8 cents on the third day, and so forth)
Exponential Functions
xbxf )(base
Variable is in
exponent
*Just because a function has an exponent, doesn’t mean it is an exponential function
Exponential Functions with Initial
Values
xbaxf )(
Initial Value,
or initial
population
Rate of
growth or
decay
Some unit of
time (usually)
Exponential Functions with Initial
Values
Initial Value,
or initial
population
Rate of
growth or
decay
Some unit of
time (usually)
trPtP 0)(
A bacteria starts with an initial count of 3000
and doubles every hour.
How many bacteria after 3.5 hours?
When will there be 25,000 bacteria?
A bacteria starts with an initial count of 3000.
An antibiotic is introduced, causing half of the
bacteria to die off each hour.
How many bacteria after 3.5 hours?
When will there be 500 bacteria?
Finding Exponential Functions
Need initial value (0, …), and another
data point (x, y).
Substitute into exponential function:
Solve for the growth/decay rate.
Then rewrite exp. function.
(similar to what we’ve done before)
xbaxf )(
Finding Exponential Functions
Find the exponential function of the
form that passes through the points
(0,100) and (4, 1600)
xbaxf )(
Finding Exponential Functions
A population of bacteria grew from 24
to 615 over the course of 5 hours, find
an exponential function to model this
growth xbaxf )(
Finding Exponential Functions
xbaxf )(
The table shows
consumer credit (billions)
for various years.
Find an exponential
function and estimate
credit for the year 2016