3.1 Notes
Precalculus Sec. 3.1 Exponential Functions
­exponential function f with base a is written as where a>0, a≠1, x is All Real numbers.
(exponential functions have the variable in the exponent position)
Graphs of Exponential Functions
­ Domain: All Real
­ Range: y>0
­ y­inter.: y=1
­ H.A.: y=0
­ Always increasing ­ Domain: All Real
­ Range: y>0
­ y­inter.: y=1
­ H.A.: y=0
­ Always decreasing 1
3.1 Notes
­ a base that appears often is e, it is called the natural number and is irrational. e≈2.718281828
­ a common use of exponential functions is compound interest
­ if you are compounding a set number of times (daily, monthly,...)
A = final amount
P = starting amount
r = rate as a decimal
n = number of times compounding/year
t = number of years ­ if you are compounding continuously (anything in nature changes continuously)
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3.1 Notes
Examples
­Identify any transformations and sketch the graph of the function
If $3900 was invested in an account that earned 3.5% interest for 4 years. How much is the account worth if it is compounded, b) continuously
a) monthly
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