[T] According to the World Bank, at the end of 2013 ( t = 0) the U.S. population was 316 million and was increasing according to the following model: P ( t ) = 316 e 0.0074 t , where P is measured in millions of people and t is measured in years after 2013. Based on this model, what will be the population of the United States in 2020? Determine when the U.S. population will be twice what it is in 2013.
[T] According to the World Bank, at the end of 2013 ( t = 0) the U.S. population was 316 million and was increasing according to the following model: P ( t ) = 316 e 0.0074 t , where P is measured in millions of people and t is measured in years after 2013. Based on this model, what will be the population of the United States in 2020? Determine when the U.S. population will be twice what it is in 2013.
[T] According to the World Bank, at the end of 2013 (t = 0) the U.S. population was 316 million and was increasing according to the following model:
P
(
t
)
=
316
e
0.0074
t
, where P is measured in millions of people and t is measured in years after 2013.
Based on this model, what will be the population of the United States in 2020?
Determine when the U.S. population will be twice what it is in 2013.
Refer to page 100 for problems on graph theory and linear algebra.
Instructions:
•
Analyze the adjacency matrix of a given graph to find its eigenvalues and eigenvectors.
• Interpret the eigenvalues in the context of graph properties like connectivity or clustering.
Discuss applications of spectral graph theory in network analysis.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]
Refer to page 110 for problems on optimization.
Instructions:
Given a loss function, analyze its critical points to identify minima and maxima.
• Discuss the role of gradient descent in finding the optimal solution.
.
Compare convex and non-convex functions and their implications for optimization.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440 AZF/view?usp=sharing]
Refer to page 140 for problems on infinite sets.
Instructions:
• Compare the cardinalities of given sets and classify them as finite, countable, or uncountable.
•
Prove or disprove the equivalence of two sets using bijections.
• Discuss the implications of Cantor's theorem on real-world computation.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]
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Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY