Suppose that a firm begins at time $t=0$ with a capital stock of $K(0)=500,000$ pesos and, in addition to

replacing any depreciated capital, is planning to invest in new capital at the rate $I(t)=600t^2$ over the

next ten years.

a$.$ What is the planned level of capital stock $K(t)$ at the end of $10$ years?

b$.$ Sketch the graph of the time path of $K(t)$ from year $0$ to year $10.($Label the points for clarity.$)$

c$.$ How much investment $($on top of replacing any depreciated capital$)$ was made between the $3^{rd}$

and $5^{th}$ year?