A young person with no initial capital invests $k$ dollars per your at an annual rate of return r$.$ Asourne that investments are made continuously and that the return is compounded continuously.

a$.$ Determine the sum $S(t)$ accumutated at any them $1.$

b$.$ If $r=7\mathrm{.}5\%,$ determine $k$ so that $1$ millioe will be available for retiresent in $40$ years.

c$.$ If $k=2000/$year$,$ determine the return rate $r$ that mat be obeained to have $1$ million walslle in $40$ years.