Question: 49. 5. During a chemical reaction, the function y = f (t) models the amount of a substance present, in grams, at time t seconds.

49. 5. During a chemical reaction, the function y = f (t) models the amount of a substance present, in grams, at time t seconds. At the start of the reaction (t = 0), there are 10 grams of the substance present. The function y = f (t) satises the differential equation % = 0.02y2. (a) Use the line tangent to the graph of y : f (t) at t : O to approximate the amount of the substance remaining at time t : 2 seconds. I2, Please respond on separate paper, following directions from your teacher. (b) Using the given differential equation, determine whether the graph of f could resemble the following graph. Give a reason for your answer. )0 '2' Please respond on separate paper, following directions from your teacher. (0) Find an expression for y = f(t) by solving the differential equation % = ().023;2 with the initial condition f(0) = 10. @ Please respond on separate paper, following directions from your teacher. ((1) Determine whether the amount of the substance is changing at an increasing or a decreasing rate. Explain your reasoning. '2' Please respond on separate paper, following directions from your teacher

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