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4.3 Use Functions Involving e
Pg 140 Part 2
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The Graph of the Exponential Function
1 3 2
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Graph natural base functions
Graph the function. State the domain and range. SOLUTION Because a = 3 is positive and r = 0.25 is positive, the function is an exponential growth function. Plug in 0 and 1. x y 1 The domain is all real numbers, and the range is y > 0.
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Graph natural base functions
Graph the function. State the domain and range. SOLUTION a = 1 is positive and r = –0.75 is negative, so the function is an exponential decay function. Translate the graph of y = right 2 units and up 1 unit. e –0.75x The domain is all real numbers, and the range is y > 1.
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Try This! Graph the function. State the domain and range. y 2e 0.5x =
domain: all real numbers, range: y > 0
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Try This! Graph the function. State the domain and range. 1 2 f(x) =
e -x +1 domain: all real numbers, range: y > 1
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Continuous Compounding Formula
A(t) = Amount (as a function of time) P = Initial Investment r = Interest Rate t = Time frame in years
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An investment of $1000 earns an annual interest rate of 7.6%
Compare the final amounts after 8 years for interest compounded quarterly and for interest compounded continuously. Compounded Quarterly Continuously
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Find the value: Of $500 after 4 years invested at an annual interest rate of 9% compounded continuously. $716.66
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Homework Notetaking Guide !!!! NTG Pg. 158, 2 – 28 Even & 29
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