Problem 5: Suppose that a species of fish (in thousands) is modeled by t + 10 0.5t2 +1' F(t) = t> 0 where t is measured in years after 2000. a. What is the initial population? b. Find F(10) and interpret its meaning. c. Find all horizontal asymptotes of F(t), if any. d. Sketch the graph of the function F(t). Label and appropriately scale the axes to include the entire graph. e. Evaluate the average rate of change of F(t) from 2004 to 2006. Interpret the meaning of your answer and include appropriate units. f. As time increases, describe what happens to the fish population. of 1

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