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)

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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/

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Classwork

• Worksheet