The total number of chickens in a farm infected with bird flu is modeled by the function 12500 Ft = 120 1 + 50e-0.12t where t is the number of days after the day an infection was first identified. (a) Determine whether F(t) is an increasing function or a decreasing function using the first derivative. Interpret what this means in the context of the problem. (b) Solve for the second derivative of F(t). Given that the only critical number of In 50 the second derivative is at t = determine the intervals where the graph 0.12 of F is concave up and where it is concave down. Interpret what these mean in the context of the problem. (c) What do you think will be the value of the lim F(t) ? Justify your answer and 1-+00 interpret this in the context of the