[8 pts] A news item is spread by word of mouth to a potential audience of 10,000 people. After t days, the number of people will have heard the news is given by: $N(t) = frac{10,000}{1 + 50e^{-0.4t}}$ a. Find the rate at which the news is spreading after 14 days. b. Approximately when will the news be spreading at the rate of 600 people per day?
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4t}} $$ To find the rate at which the news is spreading, we need to find the derivative of this function with respect to time t: $$ \frac{dN}{dt} = \frac{d}{dt} \left(\frac{10000}{1 + 50e^{-0.4t}}\right) $$ Using the quotient rule, we get: $$ \frac{dN}{dt} = Show more…
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