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Question: The function N(t), modelling the number of individuals (in thousands) infected with a certain virus...

Question: The function N(t), modelling the number of individuals (in thousands) infected with a certain virus at time t (in months since the beginning of 2019), is currently unknown. Nevertheless, it is known that on April 1, 2020, sixty{seven thousand individuals were infected with the virus and that, at that time, the number of infected individuals was increasing by ve thousand per month.

(a) Interpret the above information in terms of the function N(t) and its derivatives. Be sure to use appropriate functional notation.

(b) Construct the equation of the tangent line to the graph of N(t) at the time of April 1, 2020.

(c) Use the above tangent line to estimate the number of infected individuals on June 1, 2020. [Note: This technique of using the tangent line to estimate the values of an unknown function is called marginal analysis)

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