lecture 4.2 bt
TRANSCRIPT
Today’s Agenda
Attendance / Announcements
Sections 4.2
Quiz
Chapter 4 Exam Wednesday 3/18
More Exponential Applications
Banking – Compounded Interest
Situation: An amount (“Principal”) is deposited
into an account. An interest rate (usually growth)
is applied to the amount in the bank at specific
times throughout the year. The amount in the
bank at any time can be found using….
nt
n
rPA
1
Amount of
money in
bank
(balance)
P, amount initially
deposited, principal
r, Interest rate
(as a decimal!)
n, Number of times
compounded PER
YEAR
t, Number of
years money left
in account
Compounded…
Yearly n=1
Monthly
Weekly
Daily
n=12
n=52
n=365
Quarterly n=4
nt
n
rPA
1
Find the amount when $9000 is invested at 5.4%
compounded monthly for 6 years.nt
n
rPA
1
A total of $12,000 is invested at an interest rate of
3%. Find the balance after 4 years if the interest is
compounded quarterly.nt
n
rPA
1
A total of $12,000 is invested at an interest rate of
3%. If the interest is compounded weekly, how
long would the money need to stay invested in
order to earn $15,000? nt
n
rPA
1
Example: You deposit $5,000 into an account with a 6.5%
interest rate. Find the amount in the account after 10 years.
What happens if interest is
compounded more than daily,
hourly, every minute!?
Continuously!
nt
n
rPA
1
rtPeA
What is e ?
718.21
1lim
x
x xe
So, it’s just a
constant number
between 2 and 3!
Find the amount when $5400 is
invested at 6.25% compounded
continuously for 6 months
rtPeA
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
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The table shows
consumer credit (billions)
for various years.
Find an exponential
function and estimate
credit for the year 2016
Finding Exponential Functions
y a bx
Below is the data for the growth of some bacteria.
Using your calculator’s regression function, find an
exponential function of the form
to model this growth.
a) How many bacteria will be present after 15 minutes?
b) How long will it take for there to be 1 million bacteria?
Finding Exponential Functions
http://www.usatoday.com/story/tech/2014/10/14/m
ark-zuckerberg-facebook-ebola/17244621/
xbaxf )(
Classwork
• Worksheet