4. A store finds that its sales decline after their ad campaign ends. The rate at which the daily sales decline is given as S'(t) = 225e-0.25t days since the ads quit running. Suppose that their daily sales are 3700 units at the time the campaign ends (t= 0). Find: a. The function that describes the total daily sales, or S(t). b. What the daily sales will be 7 days after the ads stop running. - 210, wheret is the number of

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please I can really use some help to find out how to do this problem, i also provide the formula sheet i have to follow to figure it out
*TATTOO"CHEAT SHEET - USE OFTEN!
youR
THE BASICS
derrv.
PX) MP
CO) MC
RX)
X - fcx)+y ly CAN BE +,Ø,-)
Xf'cx)+SLOPE(SLOPE CAN BE +,Ø,- §Ø = MAX OR MIN OR H. P.I.})
integ
%3D
X *f"Cx) + CONCAVITY (CONCAVITY IS U,A,Ø {0iS POINT OF INFLECTION})
DERIVATIVES
PRODUCTS AND QUOTIENTS
y=x^ y'- nx^-
you"
u isA
FUNCTION,
%3D
U AND V
y=uv y'= u'v +uv
n-1
y'=nu" (u') X IS VAR.,
ARE
FUNCTIONS
y= e"
y'- u'e"
e AND ny= u y'= u'v -uv'
V
CONSTANTS
dautdin
y=Lnu y's 4
LOGS AND EXPONENTS
y=a" y'=a"u’ına ) WHERE u
IS A FUNC,
INTEGRALS
yoa" g =a*x' ina fais const,
+ X +K , n#-1
X IS VARVABLE
Fa*(1) Lna
ntl
+k, n+-1
in(e*) =x (SIMPLIFIED, NOT DERIVATIVE )
=X (SIMPUFIED, NOT DERIVATIVE)
+ e" +K
In(MN)= Ln M+ unN
in (A) - LnM -UnN
Lin(MP) =
y=lagax a =x
4- Ju'u"dx → inu tK n-
STEPS
WHERE M
EN ARE
FUNCTIONS.
(CONVERSIONS
NOT DERIVATIVES)
Pn M
WHICH INTEGRAL?
1) MAKE IT
2) FIND U; CREATE U'
3) WE HAVE
4) MAKE IT LOOK LIKE TEMPLATE
5) PERFORM INTEGRAL
PRETTY:
WE WANT.
CHANGE OF BASE:
y=loga x -LogX
= In x
loga
DEFINITE INTEGRALS
ALSO
Una
y=Sax'dx = afx*ax
y=S(ax^+bx") dx
Fa) = ffondx
JHondk = FO = F(b) - F(a)
"dx
%3D
%3D
Transcribed Image Text:*TATTOO"CHEAT SHEET - USE OFTEN! youR THE BASICS derrv. PX) MP CO) MC RX) X - fcx)+y ly CAN BE +,Ø,-) Xf'cx)+SLOPE(SLOPE CAN BE +,Ø,- §Ø = MAX OR MIN OR H. P.I.}) integ %3D X *f"Cx) + CONCAVITY (CONCAVITY IS U,A,Ø {0iS POINT OF INFLECTION}) DERIVATIVES PRODUCTS AND QUOTIENTS y=x^ y'- nx^- you" u isA FUNCTION, %3D U AND V y=uv y'= u'v +uv n-1 y'=nu" (u') X IS VAR., ARE FUNCTIONS y= e" y'- u'e" e AND ny= u y'= u'v -uv' V CONSTANTS dautdin y=Lnu y's 4 LOGS AND EXPONENTS y=a" y'=a"u’ına ) WHERE u IS A FUNC, INTEGRALS yoa" g =a*x' ina fais const, + X +K , n#-1 X IS VARVABLE Fa*(1) Lna ntl +k, n+-1 in(e*) =x (SIMPLIFIED, NOT DERIVATIVE ) =X (SIMPUFIED, NOT DERIVATIVE) + e" +K In(MN)= Ln M+ unN in (A) - LnM -UnN Lin(MP) = y=lagax a =x 4- Ju'u"dx → inu tK n- STEPS WHERE M EN ARE FUNCTIONS. (CONVERSIONS NOT DERIVATIVES) Pn M WHICH INTEGRAL? 1) MAKE IT 2) FIND U; CREATE U' 3) WE HAVE 4) MAKE IT LOOK LIKE TEMPLATE 5) PERFORM INTEGRAL PRETTY: WE WANT. CHANGE OF BASE: y=loga x -LogX = In x loga DEFINITE INTEGRALS ALSO Una y=Sax'dx = afx*ax y=S(ax^+bx") dx Fa) = ffondx JHondk = FO = F(b) - F(a) "dx %3D %3D
4. A store finds that its sales decline after their ad campaign ends. The rate at which the
daily sales decline is given as S'(t) = 225e-0.25t
days since the ads quit running. Suppose that their daily sales are 3700 units at the time
the campaign ends (t = 0). Find:
a. The function that describes the total daily sales, or S(t).
b. What the daily sales will be 7 days after the ads stop running.
210, where t is the number of
%3D
Transcribed Image Text:4. A store finds that its sales decline after their ad campaign ends. The rate at which the daily sales decline is given as S'(t) = 225e-0.25t days since the ads quit running. Suppose that their daily sales are 3700 units at the time the campaign ends (t = 0). Find: a. The function that describes the total daily sales, or S(t). b. What the daily sales will be 7 days after the ads stop running. 210, where t is the number of %3D
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