#### Transcript of 7-1: Exploring Exponential Models

**7-1: Exploring Exponential Models**

Exponential

An exponential expression is one where a constant is raised to an exponent that's a variable.

Exponential GROWTH

Exponential DECAY

Growth - getting bigger.

Exponential growth - when the constant being raised to an exponent of x is GREATER than 1

Decay - Something that decreases as time passes is decaying.

Exponential decay - when the constant being raised to an exponent of x is LESS than 1.

What is the graph of y = 4^x?

Graphing Exponential Functions

Create a T-chart of values, plot the points, and connect the dots.

What do they have in common?

What is different?

What are the y-intercepts of these functions?

Big Idea: What do Exponential Growth & Exponential Decay look like?

exponential growth?

How do you identify...

exponential decay?

What are some examples of each?

Suppose you invest $500 in a savings account that pays 3.5% annual interest.

How much will be in the account after five years?

Modeling Exponential Growth

Suppose you invest $500 in a savings account that pays 3.5% annual interest.

When will the account contain $650?

Using Exponential Growth

What do you model with these?

Formulas for Compounded Interest:

Compounded annually:

A = P(1+r)

t

Compounded n-times a year:

A = P(1 + ---)

r

n

nt

Compounded continuously:

A = Pe

rt

A = Final amount

P = Principal (starting amount)

r = interest rate (as a decimal; ex: 5% = .05

t = time

n = number of compoundings during time period

(ex: quarterly n = 4, monthly n = 12, etc.)

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