3.1 to 3.5 Answers to Review
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S HO W AL L Y O U R W O R K O N A SE P A R A T E P I E C E O F P AP ER ! !! N O A L C U L A T O R !! N a m e P re - Ca l cu lu s ( 20 0 3- 4 ) R ev iew fo r T es t C h er 3 C o m p ut e th e ex a ct va l u e of th e fu n ct i o nf o r the giv en x - va l ue. 1 . f( x ) = 7 .2 x f o r x = 1 2 . f( x )= 2 .1 44 x fo r 3. f ( x ) = 6 . 9 x f o r x = _ 4 . f( x )= 4 .2 7 x fo r W ri te t h e e x po ne n tia l f un c tio n tha t sati sfie s the g iv e n c o nd i tio n s. 5. Ini t ial p op u la ti on = 3 54 , d ou b ling e v er y 6 ho u rs . ç tC ) 6 . In itia l po p ul a tio n = 1, 4 26 , t r ipl i ng e v er y 9 ho u rs . ç o ’ 4( ’ (‘b .) ‘ 7 . I niti al ma s s = 4 ,5 9 8 gr a m s , in c rea si n g at a r a te o f 2 . 7% ccC ) ‘ . s 2 i. oaiY 8 . Ini t ial m as s 7 85 g ra m s, d e c si n g a t a ra t e o f 3. 7 % c cc th e log ari thm ic ex pr e ss i on by ri t in g it i n to e xp o ne n tial f o rm . i o g T = x X I] 10 . 1 o g 2 = x c = 6 / S 11 . 1 5. 1 og 2 = x ‘ 5 1 6. log = x V- I c5 !10 00 19 . lo g1 , 00 0 = x 20 . I n e = x q 2 1. In[ _ ) x - 2 2 . l og l O O , 0 0 0, 0 00 = x 2 3. Wr i te t h e ex pr e ssio n lo g x u sin g on ly c om m o n lo g a rit h m s. W rit e the exp re s sion 1o g x us in g o nly c om m on l og a ri th m s W r it e th e ex pr e ss i on l o g (a — 6 b) us i ng o nly n at u ra l l og a ri th m s . W ri te th e ex p re s si o n log (2 a + 8 b ) us in g o n ly n a tu r al lo ga r ith m s . As sum in g x an d y are p os i tiv e , us e p r op e rti e s of lo g a ri th m s to w rit e t he ex p re s sion as sum o r d i ff e r en c e of l o ga r ith m s o r m ul ti pl e l og a ri th m s . 28 . I n ( 4 ] 7 -j - 29. lo g J x8 y 5 X 4c X A s sum in g x an d y ar e p os i t ive , us e p r op e rtie s o f lo g ar ith m s to w rit e th e ex p re s si o n as a s i ng l e lo g ar i th m . 31 . 32 . l n x + 5 In y _ ! ln z 3 3 . 2 (l n x + ln y )_ !l n z I _ __ _ _ _ __ 5 ( _ _ --lo gx + 3l o y— 4l o gz ‘ cx t -’’_ C o m p le te the gi v en t ab l e a n d gr a ph t e fu n cti o n. 34 f (x ) =l o g x y - 1 i 0 L 1 i - r1 r x y °/ g - 2 a L ’ S ol v e 9 . 12 . lo gx =— 3 13 . ln x = 2 7 €_ 1 8 . ln x= —4 X 3 ’ 1 lo g = x 14. l o g i T = x 24 . 2 5. 2 6. 27 . 1 7. g x= 2 ‘ c c I n e x X ] 1 30 . l og (z 2 Jx 5 y8 ) 35. f (x )= l og x — 1 ) .._...L....J.
Transcript of 3.1 to 3.5 Answers to Review
8/3/2019 3.1 to 3.5 Answers to Review
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SHOW ALL YOUR WORK ON A SEPARATE PIECE OF PAPER !!!NO CALCULATOR!! Name
Pre-Ca lculus (2003-4)Review for Tes t Chapter 3
Compute the exact value of the function for the given x-value.
1. f(x)=7.2xforx=1 2. f(x)=2.144x for
3. f(x )=6 .9xforx=_ 4. f(x)=4.27x for
Write the exponential function that satisfies the given conditions.5. Ini tial population = 354, doubling every 6 hours. çtC)
6. Initial population = 1,426 , tripl ing every 9 hours. ço’ 4(’ (‘b .) ‘
7. Initial mass = 4,598 grams, increasing at a rate of 2.7% ccC) ‘.s2 i.oaiY8. Initial mass 785 grams, decsing at a rate of 3.7% ccc
the log ari thm ic express ion by riting it into exponential form.
iogT=x XI] 10. 1og2=x c= 6/S 11.
15. 1og2=x ‘5 16. log =x V-Ic5!10 00
19. log 1,000 = x 20. In e = x q
21. In[_) x - 22. log lOO, 000, 000 = x 23.
Write the expression log x using only common logarithms.
Write the expression 1og x using only common logarithms.
Write the express ion log (a — 6b) using only natural logarithms.
Write the expression log (2a + 8b) using only natural logarithms.
Assuming x and y are positive, use properti es of logarithms to write the expression as sum or difference oflogarithms or multiple logarithms.
28. In(4] 7-j - 29. log Jx8y5
X4cX
Assuming x and y are positive , use properties of logarithms to write the expression as a single logarithm.
31 . 32. lnx+5Iny_!lnz 33. 2(lnx+lny)_!lnzI
____ ____
5 (
__
--logx+3loy—4logz‘cx t-’’_
Complete the given tab le and graph the function.
34 f(x)=log
x y
-1
i 0
L, 1
i-r1 r x y
°/g -2
a
L’
Solve
9.
12. logx=—3 13. lnx=2 7 €_
18. lnx=—4 X 3’
1log = x
14. logiT=x
24.
25.
26.
27.
17. logx=2 ‘cc
Inex X]
30. log (z2Jx5y8)
35. f(x)=logx—1)
.._...L....J.
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YOU MAY USE A CALCULATOR NamePre-Calculus (2003-4) ---Review for Test Chapter 3.1 — 3.
Determine a formula for the exponential function whosevalues are given in the table or whose graph is shown.1. 2.
x f(x)
-2 1.667
0 15
2 135
x f(x)
-2 10
0 22.5
2 50.625
4. The number P of students infected with flu t days after exposure is modeled by P(t)=
1+e -a) What was the initial number of students infected with the flu? -..-9b) How many students were infected after 2 days? “-O
C) When will 250 students be infected? .k dG.s *
d) What would be the maximum number of students infected?
5. The population of Metroville is 257,000 and is decreasing by 2.1% each year.a) Write a function that models the population as a function of time t. LO scc (b) Predict when the population will be 170,000. 413
6. The population of Preston is 86,000 and is increasing by 1.4% each year.a) Write a function that models the population as a function of time t. cct): co ( o 4)b) Predict when the population will be 92,000. 4 4 .u
Solve each equation algebraically. SHOW YOUR WORK!!! Obtain a numerical approximation for your solution.Round your answer to the thousandths.
8. 34e =178
10.32
=14 11. logx—3)—5=3 c’j
13. 36e =180 14. 2(8)6 =86 O’33
16. logx—4)+12=16 17. In(3x+1)I1n(x_2)=1n(2x2+4x_4) q--FT3
19. State whether the function y = ex_ —2 is an exponential growth or an exRonential decafuicion and
describe its end behavior using limits. Lcou —
20. State whether the function y = 2ex +4 is an exponential growth or an exponential decay function and
describe its end behavior using limits. Cc) 4 lC Ric)
For 21 & 22, graph the given function (be sure to plot at least 2 points exactly) and analyze it for its domain,range, asymptotes, and describe its end
21. f(x)=log4x)
3. Find the logistic function that satisfies thegiven conditions:
A) Initial value = 45, limit to growth = 450,
passing through (2, 225).-
‘
B) Initial value = 100, limit to growth = 700,passing through (2, 280)..
‘f .4-t(
7.(345)X
= 10.25 j%219
18. In(2x+4)+In(x_1)=ln(x2_10x+19) _i-4sq
9. 7(5) =94
12. 2.45x =9.25
15.5X+2
9 —
Domain:Rinnp
behavior using limits.
22 .
Asymptotes:End Behavior: b’ r ç’Cx.)
‘iw’ Etc)
i4 •L%.4
.1jL i:
f(x) = log (16x)
Domain: W>ORange:Asymptotes: 0
End Behavior: —
4i —
Li..
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