Revenue: Target The annual revenue earned by Target for fiscal years 2004 through 2010 can be approximated by R ( t ) = 41 e 0.094 t billion dollars per year ( 0 ≤ t ≤ 7 ) , where t is time in years. ( t = 0 represents the beginning of fiscal year 2004.) Estimate, to the nearest $10 billion, Target’s total revenue from the beginning of fiscal year 2006 to the beginning of fiscal year 2010.
Revenue: Target The annual revenue earned by Target for fiscal years 2004 through 2010 can be approximated by R ( t ) = 41 e 0.094 t billion dollars per year ( 0 ≤ t ≤ 7 ) , where t is time in years. ( t = 0 represents the beginning of fiscal year 2004.) Estimate, to the nearest $10 billion, Target’s total revenue from the beginning of fiscal year 2006 to the beginning of fiscal year 2010.
Solution Summary: The author calculates the Target's total revenue from beginning of fiscal year 2006 to 2010, where the annual net revenue is approximated by R(t)=41e0.094t
Revenue: Target The annual revenue earned by Target for fiscal years 2004 through 2010 can be approximated by
R
(
t
)
=
41
e
0.094
t
billion dollars per year
(
0
≤
t
≤
7
)
,
where t is time in years. (
t
=
0
represents the beginning of fiscal year 2004.) Estimate, to the nearest $10 billion, Target’s total revenue from the beginning of fiscal year 2006 to the beginning of fiscal year 2010.
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
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