2. During a chemical reaction, the function y = f(t) models the amount of a substance...

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2. 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) satisfies the differential equation = -0.02y². dy dt (a) Use the line tangent to the graph of y=f(t) at t = 0 to approximate the amount of the substance remaining at time t = 2 seconds. (b) Using the given differential equation, determine whether the graph of f could resemble the following graph. Give a reason for your answer. (c) Find an expression for y=f(t) by solving the differential equation condition f(0) = 10. (d) Determine whether the amount of the substance is changing at an increasing or a decreasing rate. Explain your reasoning. -0.02y2 with the initial dt 2. 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) satisfies the differential equation = -0.02y². dy dt (a) Use the line tangent to the graph of y=f(t) at t = 0 to approximate the amount of the substance remaining at time t = 2 seconds. (b) Using the given differential equation, determine whether the graph of f could resemble the following graph. Give a reason for your answer. (c) Find an expression for y=f(t) by solving the differential equation condition f(0) = 10. (d) Determine whether the amount of the substance is changing at an increasing or a decreasing rate. Explain your reasoning. -0.02y2 with the initial dt