Reference no: EM132388907

Question 1. (a) Your credit card from a dubious source penalizes you, when you default, using continuous compounding on what you owe at 20%. How long will it take for your $15,000 debt to mushroom into $50,000?

(b) Assuming that cash-flows should be discounted at a rate of 0.1 per year, what is the Net Present Value of the following expected cash flows shown below

Yesr	1	2	3	4	5
Revenue	80	-40	100	100	150

(c) Compute the Intenal rate of return (IRR) for an investment with the following cash-flows. Investment now = $1000. The expected returns at the end of every year for the next 6 years, respectively, are: -$250, $200, $400, $350, $250, $300.

Question 2. Consider an ecological niche with three species A, B and C. Their dynamics are given by their population rates shown below

dA/dt = A + B - C ....(a)

dB/dt = A + 2B     ....(b)

dC/dt = C -A - B ....(a)

Initially, the niche is in equilibrium with the population of C = 30. Obtain the population densities of the rest of participants in the niche at its equilibrium. Starting from the point

(A = 8, B = 4, C = 10), obtain their individual populations overtime:. What if the initial starting point is perturbed to (A = 7, B = 4, C = 10)? Would the system emerge in the same way?

Question 3. What phase portrait or phase diagram is all about? What information does it convey to the analyzer? Obtain the phase portrait of the system of differential equations using quiver distribution

dx/dt = x(3x - 7y -2)

dy/dt = y(x + y -2)

What conclusion do you derive from your quiver distribution?

Question 4. Consider our romantic duo Romeo and Juliet, and their love for each other as manifested by the general equations over the variables R and J shown below (with initial values R = 5, J = 5)