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Consider \(y’+y=2e^t\). We’ve already done the integrating factor step for you and rewritten the ODE as $$(e^{t}y)’=2e^{2t}$$ Finish solving for y.

A population is modeled by \(P(t)=\frac{{12}}{{2+2e^{{-12t}}}}\). Compute \(\lim_{{t\to\infty}}P(t)\). What happens to the population in the long term?

A population is modeled by \(P(t)=\frac{{12}}{{2+4e^{{12t}}}}\). What happens to P(t) as t increases?

What does American mobilization during World War I reveal about the changing relationship between the federal government and American society?

What was the broader cultural importance of the Harlem Renaissance?

Why did unrestricted German submarine warfare contribute significantly to the United States entering World War I?

The resurgence of nativism during the 1920s can best be understood as a response to which combination of factors?

The Great Migration during World War I is best understood as

Why were the Sixteenth and Seventeenth Amendments important to Progressive reform?  

Which example best demonstrates a major limitation of Progressive reform?