Today’s Agenda

Attendance / Announcements

Sections 4.1b / 4.2

Quiz Friday

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

Find the amount when $9000 is invested at 5.4%

compounded monthly for 6 years.

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.

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

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

Classwork

• Worksheet