During a recession, Congress decides to stimulate the economy by providing funds to hire unemployed workers for government projects. Suppose that t months after the stimulus program begins, there are N(t) thousand people unemployed, where

a. What is the maximum number of unemployed workers? When does the maximum level of unemployment occur?

b. To avoid overstimulating the economy (and inducing inflation), a decision is made to terminate the stimulus program as soon as the rate of unemployment begins to decline. When does this occur? At this time, how many people are unemployed?

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N(t) = −³+ 45t² + 408t + 3,078