1. [5] Recall from calculus that y(x) = Ae** is the solution of the differential equation...

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1. [5] Recall from calculus that y(x) = Ae** is the solution of the differential equation y' = ky, y(0) = A, where A and k are constants (for a given problem). Note that although A and k are constant for a given problem, they can change from problem to problem, thus act as "parameters" for this differential equation. The solution here is referred to a "closed form" since we can explicitly write in terms of the parameters and find the solution for a given A and k without resolving the differential equation. Examine how each of these parameters affects the solution. (a) Graph the solution for various values of A. How does the solution change (if it does)? (b) Do the same for various values of k (positive and negative). How do these values affect the solution? Summarize your results. [Note that there are a variety of online applications, like Desmos, that allow not only graphing these functions, but setting up real-time variation of parameter values using sliders.] 1. [5] Recall from calculus that y(x) = Ae** is the solution of the differential equation y' = ky, y(0) = A, where A and k are constants (for a given problem). Note that although A and k are constant for a given problem, they can change from problem to problem, thus act as "parameters" for this differential equation. The solution here is referred to a "closed form" since we can explicitly write in terms of the parameters and find the solution for a given A and k without resolving the differential equation. Examine how each of these parameters affects the solution. (a) Graph the solution for various values of A. How does the solution change (if it does)? (b) Do the same for various values of k (positive and negative). How do these values affect the solution? Summarize your results. [Note that there are a variety of online applications, like Desmos, that allow not only graphing these functions, but setting up real-time variation of parameter values using sliders.]