4.3 Use Functions Involving e

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Presentation transcript:

4.3 Use Functions Involving e Pg 140 Part 2

The Graph of the Exponential Function 1 3 2

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.

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.

Try This! Graph the function. State the domain and range. y 2e 0.5x = domain: all real numbers, range: y > 0

Try This! Graph the function. State the domain and range. 1 2 f(x) = e -x +1 domain: all real numbers, range: y > 1

Continuous Compounding Formula A(t) = Amount (as a function of time) P = Initial Investment r = Interest Rate t = Time frame in years

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

Find the value: Of $500 after 4 years invested at an annual interest rate of 9% compounded continuously. $716.66

Homework Notetaking Guide !!!! NTG Pg. 158, 2 – 28 Even & 29