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Unformatted text preview: 2. We can graphically determine the derivative of ex . Draw f ( x ) = e x and g ( x ) = ex on the axes below. Demonstrate in your drawing that the slope of g ( x ) at x is the negative of the slope of f ( x ) atx . That is, g ( x ) = . (Check with problem 15 on page 224.) A population of wolves increases so that the number of wolves x years from now is given by the function W ( x ) = 200(1ex ). Calculate W ( x ). At what rate does the population change after 1 year? 3 years? (Include units and round to the nearest tenth). Sketch the graph of W ( x ) for x ≥ 0. Label any asymptotes and intercepts. Evaluate lim x →∞ W ( x ) and lim x →∞ W ( x ). What is the interpretation of these limits in terms of the wolf population and its growth rate as time passes (to inﬁnity). 2...
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 Fall '08
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 Calculus, Derivative, Continuous function, horizontal tangent lines

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