This is my mid paper please solve correctly Subject Name: Algorithms Practical q

Question

This is my mid paper please solve correctly

Subject Name: Algorithms

Practical questions such as "how fast does a disease spread? Or how fast does a population change" involve rates of change or derivatives. Company XYZ is a start-up company, but its client base is in fast growth mode. The revenue growth rate y can be stated as following differential equation dy/dx=0.2*x*y y(1)=1 (a) please write computer code to implement the Euler's algorithm to obtain company's revenue when number of clients hit 7. One may use 0.05 as step size to do recurrence. (b) please write computer code to implement the Fourth order Runge-Kutta algorithm to obtain company's revenue when number of clients hit 7. One may use 0.05 as step size to do recurrence. (c) please solve this differential equation analytically and find the exact answer of y(7). (d) what are % errors of the Euler's algorithm and the Fourth order Runge-Kutta algorithm, respectively, as comparing with exact solution?

Explanation / Answer

(a)

(b)

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