E/
K
*^^"
Block-Date
lntroto Calc
Functions
Exponential
growthfunction
or exponential
is anexponential
thefunction
ln Exercises
1-6,tellwhether
percentage
rateofgrowthor decayforthefunction.
andfindtheconstant
decayfunction,
1.
ot7"
%tvwl^
f (r) = 4.3 ol.0L8'^,co
arvtril4..' I "',6 /a
2.
f(*)=3.5o1.09'
U
tl
3.
f(*)=7896310.968'
4.
f"r{*tw
( *)=2 4 7 t2 '
6.
f(x)= 5607o 0.9968'
datrqc.#%
3,?%
furu,.t
5.
f( *) = 43o0.05'
t()dk
dacai/ 95"7c
thegivenconditions.
function
thatsatisfies
7-18,findtheexponential
In Exercibes
7.
Initialvalue= 5, increasing
at a rateof 17%peryear
8.
ata rateof2.3%perday
fnitialvalue= 52,increasing
-^1t'iX
--./
,- /, ,-\x
y t t (t't r1
oc
q=57(t,o?3)
9.
g=tU(.s)"
X=*o€ mctv\'{4'5
or y=ttr(.s)^
s("qq4,)nt
tr
= 5 (. ql| l)x X' il {,^,.otu
I
--soJlooo
Q,al7)"
= 28,900,decreasing
at a rateol2.6Y"peryear
fnitialpopulation
1=
13.
X=#oF
a\s
= 502,000,
at a rateof 1.7%peryear
increasing
Initialpopulation
y
12.
3=54(l,Da3)
week
at a rateof0.59%per
Initialvalue= 5,decreasing
J=
11.
-\x
at a rateof50%permonth.
Initialvalue= 16,decreasing
, -11?X
10.
-n/,
(,qlq)"
a?,qca
lnitialheight18cm,growingat a rateof 5.27oPerweek
3
= Is(t oudtx.'r
w (L'osef
X ={ o( v"en-k*5
14.
fnitialmass= 15g,decreasing
at a rateof 4.6%perday
!v
6( ,l=tS(,?sq) x -- l Iur c2t. r
y=tS(,q54)tot'
I
tu\s
15.
Initialmass= 0.6g,doubling
every3 days
.7: , {o (}-)at*/s/
I
16.
=250,doubling
fnitialpopulation
every7.5hoursg lbohrs/,4o,'
\\ // -- * ^crl rc\'/Jo \ ll t*u) { X
I
17.
Initialmass= 592g,halving
onceevery6 years
u: 5q]('til'r'
I
18.
Initialmass= 17g,halving
onceevery32hours
-
r*-.,/tt^=\a 73,' li.X
t / ('/"] )
\/:
I
In Exercises
19'20,determine
a formula
fortheexponential
function
whosevaluesare
givenin the Table,
_1T
-2
- I
0
|
2
19,
1=
st',4
fG)L?
1.472
1.84
2.3
2.875
3.s9375
- ?,,1t',1
-9.0625
_7.25
'
y ' * r , ( r , , 13' th
-4.U
-3.712
b.. -,?t i
za. g(x) q = S,t e
^' 'u(l'as)Y
?b
, (!Ll : ('t:'
-5.8
f(x)
i;: 'ff €-
't?ex
J
|nExercises21and22,determineaformu|aforthe-@whosegraphis
showninthefigure.
21.
22.
--'" ':
$ci;..s,2':,
J - qoqv
rL
,r.,
'- \-
!^.t ,r-'t>
i )(Jr(Jr(rr'f
)U
a'J-
C
*l
,i- : lsllb
0t\0 L
! 1 1 4 1 : . J : ' u iS
5P
)t
. - i.ool
L{ev
0 "''
!:
lb
4^('1tr\';
b
--- ,iqy
3=