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 dy present. The function y = f(t) satisfies the differential equation = -0.02y?. 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. wold gg No beo nt dy (c) Find an expression for y = f(t) by solving the differential equation = -0.02y? with the initial condition f(0) = 10. %3D %3D dt. %3D (d) Determine whether the amount of the substance is changing at an increasing or a decreasing rate. Explain your reasoning.

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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
dy
present. The function y = f(t) satisfies the differential equation
= -0.02y?.
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.
wold
gg No beo nt
dy
(c) Find an expression for y = f(t) by solving the differential equation = -0.02y? with the initial
condition f(0) = 10.
%3D
%3D
dt.
%3D
(d) Determine whether the amount of the substance is changing at an increasing or a decreasing rate.
Explain your reasoning.
Expand
Transcribed Image Text

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 dy present. The function y = f(t) satisfies the differential equation = -0.02y?. 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. wold gg No beo nt dy (c) Find an expression for y = f(t) by solving the differential equation = -0.02y? with the initial condition f(0) = 10. %3D %3D dt. %3D (d) Determine whether the amount of the substance is changing at an increasing or a decreasing rate. Explain your reasoning.

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