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ltf,'IMaster of Economics ior Professionals
MEc 2od Batch l't Semester
MEc 503: Mdffiematics for Business & Economics
For Topic 2 (Exponential & Loearithmic Functions)
1. For y : b* , we assume that b >1. How will you justifu that assumption?
2. Draw the graphs for the following functions:
(a) y : b', (b)y: bz*, (c)y= b-*, . (d)y: b-2', (e)y: Sbx, (Dy : 5b2*,
(g) y: 5b-', (h) y: 5b-2', (i) y = -5b', 0) y = -sb2', G) y: -sb-',(l) y: -5b-2t, (m) y: 560'5x, (n) y= -560'5x, (o) y= 56-05x, fu)y: -56-0'sx.
What positional relationship do the graphs display? Do they the same y intercept? How?
3. Convert the following functions into natural exponential functions.
(a) y: 6*, (b) y: 62', (") y: 5(6)', (d) y: 5(7)2*, (e) y: 5(9)-2', (D y: -5(3;-o's'.4. Convert the following functions into natural logarithmic functions.
(a) y : 6t, (b) y: 6'', (")t :log2y, (d) t:7logn}y, (e)t:lo96 3y, (0 t: 3log15 9y.
5. Use the following functions to find out the value of 'x'.
(a) 4sz'-t's = 360, (b)|e'2:259, (c) ln (x + 4)z = 3, (d) fn (rffi) = 2.55
For question 6-7,you are given that, P = 1000, r = llYo, and t : 5 years.
6. Calculate the value to be received (S) when compounded (a) annually, (b) semiannually,
(c) quarterly, (d) monthly, and (e) continuously.
7.' What is effective annual rate of interest? Calculate the effective annual rate of interest in
each case above.
8. Calculate the amount that you should invest now to get 15000 after 5 years from now at
l0% interest rate when compounded (a) annually, (b) semiannually, (c) quarterly,
(d) monthly, and (e) continuously.
9. Given P: 1000, r: l0%o, and t = 5 years, use natural exponential function to calculate
the value to be received (S) when compounded (a) annually, (b) semiannually,
(c) quarterly, and (d) monthly.
10. Given P : 1000, S : 1800 and t: 5 years, find out the rate of grgwth when compounded -
(a) annually, (b) continuously.
: l*'
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t-.-+'F i€.|*r
I l. Determine the interest to have money treble in 6 years when compounded
(a) annually, (b) , (d) monthly, and (e) continuously.
12. How long will it take Ie at 12 percent interest when compounded
(a) annually, (b) semiannu#y,{@ tparterly, (d) monthly, and (e) continuously?
13. Find out the growth rates fo1&o'b*bwing functions:
(a) Y : tlt Aes'ffi , (b)Y= te'tz, (c)Y :t3etz
!:1.*:F**:f :N.*:1.***rlrl.{.{.* NOTICE rFrFrl.**,1.*{.X.**{.****d.,k***,F**********{.,1.*
We will have a tutorial session (will work on the two practice sheets) on the opening day after
your autumn vacation (November 02, 05:4f-07:00 PM). You all are requested to bring your
scientific calculator and a printed copy of both practice sheets. If you have any problem
regarding my parts, please feel free to meet me at the scheduled time as follow:
Md. Moniruzzam n
October 14,2015
{
( &r Time F.tpom
Monday 11:00 am - 04:00 pm 328 Email: mz [email protected]
Tuesday 11:00 am - 05:00 pm 328 Cell: 01723528538
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lo.lbte, l= bn
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!= PCe+ +f*, t(6
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t2 e
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2
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. e,N, In \ _Ir- IL
i -- 2{t/eL"l-n,
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, -9x6
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n l/v\
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: .vuln3=)e
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,, -Y'ulnb -L=) '/q= e
, Ylzrl.'^9 ,r \
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O irlarrlA/1 ("t= tp^-v-t< , -ro(
J= p(+fl , .y'/,f
=) l-P= P Ln* +)>) 3: q* '/f_̂lty
)
)
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\ = L'L;/*L"e -11
2
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=) 32 e'
i LtL
) l-Y = Iqe
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) L'rb -- 6n-
Page 19
@Hesre, P=P, 9= ttP
,t L/.
@ #nn u^LlJ @ --9'rZl;/D
s -' PLt*
=> '1P = pLr*f!)t*t
ln t'rz-
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g, P U* ;1)** o*
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+ ,l?= ? (r* -T) ,n
=) ,t, Q4 o''2
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, ln I = l^ l'oe)
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Page 20
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2.t47-PJ7"4
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ttt=. rnLgg
, /n'l
--
L ' \/n(roz;
g= P( r* i^fn ryt
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=)>-+21_-=
=) [n?=
2 l"?') t,
g ,/-*Ab (n-- tz)
tc-t
,!."', Lo9
tL,[ /nUo,
{
L^'tt 2-lnQol)
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9 (r-hr,/crlL@
g = peo,,tZL
? 4P= ? Q ,
'l z-t
2 7-- e
-/
22
t 'lUt!r'l = ln e
!- rt = ,tz( lne
lr^7 = 'lLt'l't ?
@5-1 0
Y={a Ae
, 5-40\.r- a-Z Ael-
s_<6)
,) !^/ -- l, (n'" A e '/
) l*,/ = lnLl'+ /'F * I^i'{t
) t^/ -- h!'^€ + ("'R + Qtf ("e
= -t.r-[^t -tl'n(l *Q ko)
.:Kg= P
Page 22
@
+
=)
)
)
Y = 1"d"/ -- .(,3 ul-
!n'l =
)n/=
l^/ --
ln/ =
'- */=
hat9l^t + lnnnl'
'\nt + o(n '!'ne-
.lnt + n("
A ll^/)d+
lL + 2-nt
= '9r: + z+
= 3/+ +z-+
) !"n/ = /^ Llt t*)
) h7 = l^ls+ A"*'+-1t'-- **i-r-(r'(n4 = gtnt*("
e tt..nJ= bW|
A (gL^t t€)= de \
*br)-' %/) Yl *=/a+2,c1
d.vf,t<J
= !1, +utLI
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