



 
Hi, The function that is used to model this rumor is \[f(t) = \frac{70}{1 + 3 e^{0.2 t}}\] where $t$ is the number of hours after the rumor was started and $f(t)$ is the percentage of people who have heard the rumor at time $t.$ Substitute $t = 2$ and use your calculator to evaluate $f(2).$ I got a little over $23 \%.$ Use the calculus you know to obtain $f'(t)$ and then calculate $f'(2).$ This will tell the rate at which the rumor is spreading at time $t,$ in percentage per hour. The last sentence asks you to evaluate the limit of $f(t)$ as $t$ approaches infinity. You know that as $t$ approaches infinity $e{t}$ approaches zero, so this limit is straightforward to evaluate. This limit is a percentage. What does it represent? Penny  


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