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  3. 2 3 points total 1 point each before working this...

Question: 2 3 points total 1 point each before working this...

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2. (3 points total; 1 point each) Before working this problem, read the box on page 99 of the textbook. The rate of growth over time of some variable X, %AX, is just (new X-old X)/(old X)-AXX. Calculus! The rate of growth over time of X is also equal to the derivative of In(X) with regard to time Let t stand for time. Remember the chain rule Remember the derivative of In(X) 1/X And remember: a derivative is just change, so dX/dt is the change in X over the change int. And thug we havedoa da) ax 1 a.Aover And thus we have, growth rate of x Use the rules of natural logs and calculus to show that the rate of growth over time of a product oftwo variables, Xy, is the sum of the rates of growth of the variables x and y. a. Use the rules of natural logs and calculus to show that the rate of growth over time of a quotient of two variables, xły, is the difference between the rates of growth of the variables x and y. b. Use the rules of natural logs and calculus to show that the rate of growth over time of a variable x raised to a constant power b, x, is the constant b times the rate of growth of the variable x. c.

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