Marketing. An automobile company is ready to introduce a new line of hybrid cars through a national sales campaign. After test marketing the line in a carefully selected city, the marketing research department estimates that sales (in millions of dollars) will increase at the monthly rate of S ′ ( t ) = 10 − 10 e − 0.1 t 0 ≤ t ≤ 24 t months after the campaign has started. (A) What will be the total sales S ( t ) t months after the beginning of the national campaign if we assume no sales at the beginning of the campaign? (B) What are the estimated total sales for the first 12 months of the campaign? (C) When will the estimated total sales reach $100 million? Use a graphing calculator to approximate the answer to two decimal places.
Marketing. An automobile company is ready to introduce a new line of hybrid cars through a national sales campaign. After test marketing the line in a carefully selected city, the marketing research department estimates that sales (in millions of dollars) will increase at the monthly rate of S ′ ( t ) = 10 − 10 e − 0.1 t 0 ≤ t ≤ 24 t months after the campaign has started. (A) What will be the total sales S ( t ) t months after the beginning of the national campaign if we assume no sales at the beginning of the campaign? (B) What are the estimated total sales for the first 12 months of the campaign? (C) When will the estimated total sales reach $100 million? Use a graphing calculator to approximate the answer to two decimal places.
Marketing. An automobile company is ready to introduce a new line of hybrid cars through a national sales campaign. After test marketing the line in a carefully selected city, the marketing research department estimates that sales (in millions of dollars) will increase at the monthly rate of
S
′
(
t
)
=
10
−
10
e
−
0.1
t
0
≤
t
≤
24
t months after the campaign has started.
(A) What will be the total sales S(t) t months after the beginning of the national campaign if we assume no sales at the beginning of the campaign?
(B) What are the estimated total sales for the first 12 months of the campaign?
(C) When will the estimated total sales reach $100 million? Use a graphing calculator to approximate the answer to two decimal places.
3. Consider the following theorem:
Theorem: If n is an odd integer, then n³ is an odd integer.
Note: There is an implicit universal quantifier for this theorem. Technically we could write:
For all integers n, if n is an odd integer, then n³ is an odd integer.
(a) Explore the statement by constructing at least three examples that satisfy the hypothesis,
one of which uses a negative value. Verify the conclusion is true for each example. You
do not need to write your examples formally, but your work should be easy to follow.
(b) Pick one of your examples from part (a) and complete the following sentence frame:
One example that verifies the theorem is when n =
We see the hypothesis is
true because
and the conclusion is true because
(c) Use the definition of odd to construct a know-show table that outlines the proof of the
theorem. You do not need to write a proof at this time.
matrix 4
Please ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.
Chapter 5 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
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