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7-1: Exploring Exponential Models

Algebra 2 Honors
by

Jessica Edrington

on 9 April 2014

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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.)
Full transcript