Jim starts to work in January - time k=0. His income was zero the previous six months. His income is steady and constant for 0<= k <= infinity. His income is u(k) - the unit step. The unit, whether it is 5'000 K$, or 10'000 K$ is not known.
Let x(k) be his monthly income. His spending strategy is to spend in month k- the average of his income over the past seven months, i.e.
y(k)= (1/7)* [ x(k)+x(k-1)+......+x(k-6)]
1 Tabulate his spending y(k) for 0 <= k <= 10
2 Plot his spending function y(k) versus k.
3 Is he overspending or under-spending? Why? Explain.