Exponential Growth and Decay Functions

Name ------------------------ Date ____ Exponential Growth and Decay Functions Essential Question What are some of the characteristics of the graph of an exponential function? EXPLORATION: Identifying Graphs of Exponential Functions Work with a partner. Match each exponential function with its graph. Use a table of values to sketch the graph of the function, if necessary. a. /� � o d. /(x) = u-t 2x C. )( (1>1 : I ° '2. I� I f(x) = 4x (x 1.i,';.1,,t D •f O;;' i, (½J f( = D X V o � l ;-I -t I j. I� J. ·;..tS B. . .]= 2 4 X .. ·•· _ :VA -T- ---t-t--t----1-,-1 -� - f: ,-1- 5 -, _ f- 4 l--ll-1--1--.--+--I ,-,-- I t--t---+-·1--t--t- 2 �. � l -4 i ,,-+-+--+-4--t-l 1 - ../ -2 ' ....J.......L� . . . . ...x Name ________________________ Date ---- Notetaking with Vocabulary For use after Lesson 6.1 In your own words, write the meaning of each vocabulary term. exponential growth function b >I b,'3"-j� r�vi 1 /f �o,� fo f'� n5'1t f- b growth factor ''6'' ft..e._ Ji. f,µs e"'--ch o(,/fp vi asymptote fk v�l� fk t1M"l1 n �?f rc,t1c)�':- b0+ nfv,t,r 1-oµ c tV)s +- ts r.1�/f.pl,.,,, i. by. exponential decay function 6 AS L I b�� b >o ( D Lb LI} sf,\� 11 Core b"'-1- pc,s1-kw Concepts Parent Function for Exponential Growth Functions The function f(x) = bx , where b > I, is the parent function for the family of exponential growth functions with base b. The graph shows the general shape of an exponential growth function. y f(x) = bX·--------.. > 1) The grapltl'i�es from left to right, passing (1 ' b} The x-axis is an asymptote of through the points the graph.An asymptote is a 1-+-4---===----1 -----+-l (0, 1) and (1, b). line that a graph approaches more and more closely. (b TJ1e domain of f(x) = b.r is LI real number The range is y > 0. )<- VC1 I �5, q... , (1;1\1\.+� dor1 . rtt,+e.. • w.fud.t., fLe... � symp Name __________________________ Date ____ - Notetaking with Vocabulary (continued) Parent Function for Exponential Decay Functions The function f(x) = b x , where O < b < 1, is the parent function for the family of exponential d.:g_ay functions with base b. The graph shows the general shape of an exponential decay function. y f(x) = bx The graph *from left to right, passing through the points (0, 1) and (1, b). (0 < b < 1) The x-axis is an ____:_.:.....:.+-==--.� ◄- asymptote of the graph. The domain of f(x) = bx is all real numbers. The range is y > 0. Compound Interest Consider an initial principal 1' deposited in an account that pays interest at an annual·rate r (expressed as a decimal), compounded n times per year. The amount A in the account after t years is given by t,/ � ff1 l\li P" i ��,� ''•"- i k" I 1\ A - f(I + ! J r· :: r� �e... •·" "'4.ciwi1t I r::.. 't '7o -I,) .oq r- � 12,.;'70 4. 12. '" =� �.5% -� ,o,rs- ( " � y �IA, '' $ t,M 1 -� NHt �. I q�wly Mar\'rA \y ( f\ ; 2 Name _________________________ Date ---- - Notetaking with Vocabulary (continued) Extra Practice In Exercises 1-4, tell whether the function represents exponential growth or exponential decay. Then graph the function. 2. 0 -l y = ?\ (1.sr C1row+'V\ 4. f- y = (o.sr Dec�y l (t"l,f -1 -;:� (J'\ 2,. , _J_.l---1----f---' 1 __ 1-1 � --·= . ._,_L_��__, --1., 1---t--t--+-+--t 5. The number ofbacteriay (in thousands) in a cult:C: cai�e•�proximated by the model y = lOO(t.99)', where t is ( 1; c;" r 1 1 the number ofhours the culture is incubated. a. Tell whether the model represents exponentiaLgrowtb or exponential decay. --· b. Identify the hourly percent increase or decrease in the number ofbacteria. c.�hen the number ofbacteria will be 1,000,000. In Exercises 6 and 7, use the given information to find the a,Tount Ji in the account earning_l __ compound}n� rest after 5 year� hen the principal is'l� 25�. •• � � ( ·/ 6. r = 4;2'5%, compounded �u�erly ; 7. r = ,L.25%, compoundedHl�� nffiiJy:! . t �-c�t- l-/� r;. Jt + � -=