Suppose that: The number of unemployed adults in the US decreased by 100, 000 during the month of January. The number of unemployed adults in the US decreased by 70, 000 during the month of February. • The number of unemployed adults in the US decreased by 40, 000 during the month of March. • The number of unemployed adults in the US decreased by 10,000 during the month of April. Let N(t) be the number of unemployed adults t month after the beginning of the year. (So t = 0 means Jan 1st, t = 1 means Feb 1st, t=2 means March 1st, etc.….). (a) What would N(t) looks like? Sketch a possible graph for N(t). N

Suppose that: The number of unemployed adults in the US decreased by 100, 000 during the month of January. The number of unemployed adults in the US decreased by 70, 000 during the month of February. • The number of unemployed adults in the US decreased by 40, 000 during the month of March. • The number of unemployed adults in the US decreased by 10,000 during the month of April. Let N(t) be the number of unemployed adults t month after the beginning of the year. (So t = 0 means Jan 1st, t = 1 means Feb 1st, t=2 means March 1st, etc.….). (a) What would N(t) looks like? Sketch a possible graph for N(t). N

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

Question

6.
Suppose that:
• The number of unemployed adults in the US decreased by 100,000 during the month of January.
• The number of unemployed adults in the US decreased by 70,000 during the month of February.
• The number of unemployed adults in the US decreased by 40, 000 during the month of March.
• The number of unemployed adults in the US decreased by 10, 000 during the month of April.
Let N(t) be the number of unemployed adults t month after the beginning of the year.
(So t = 0 means Jan 1st, t = 1 means Feb 1st, t=2 means March 1st, etc...).
(a) What would N(t) looks like? Sketch a possible graph for N(t).
N
0 1 2
3
4
(b) True or False?
Remark: For this question to make sense we need to make the additional assumption that N(t) is smooth (no sharp corner on the
graph) and that N(t), N'(t) and N"(t) do not change sign on the interval (0,4].
• N(t) is positive on the interval [0,4] True
• N'(t) is positive on the interval [0,4]
N"(t) is positive on the interval (0,4]
• N(t) is increasing on the interval [0,4]
• N'(t) is increasing on the interval (0,4] True
False
True
False
True
False
True
False
False

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