Q1. Given that the function

y1=e-1.2xsin(10x+5)

and

y2=x3-100

Write MATLAB to plot y1 for 0x5 and y2 for -6x6 on the same figure (divided into two sections). Indicate clearly the graph components.

Q2. The Explicit Euler Formula:

Let dS(t)dt=F(t,St) be an explicitly defined first order ODE with interval to,tf with spacing h. Without loss of generality, assume that to=0 and tf=Nh for some positive integer values N. The linear approximation of St around tj and tj+1 is given by

Stj+1=Stj+(tj+1-tj)dS(tj)dt

or equivalently

Stj+1=Stj+hF(tj)S(tj)

Consider the differential equation df(t)dt=e-t with initial condition f0=-1 has the exact solution f(t)=-e-t . Use MATLAB code to approximate the solution to this initial value problem between 0 and 1 in increments of 0.1 using the Explicit Euler Formula. Then, plot the difference between the approximated solution and the exact solution.

Q3. Given the following discrete time equation

yn+14yn-1-18yn-2=x[n]

Assume the initial values y[0]=0; y[-1]=0. Solve the given equation and plot the graph. Present the work in MATLAB.

Q4. Determine how long it will take to accumulate at least $10,000 in a bank account if you deposit $500 initially and $500 at the end of each year, if the account pays 5% annual interest. Write the MATLAB code to perform the task.

Q1. Given that the function yl = 8-1.28 sin (10x + 5) and y2 = |x-1001 Write MATLAB to plot yl for 0