$(10$ pts$).$ If the steady state consumption per worker, $c^{**},$ is $$450$ billion, the depreciation rate, $,$ is $12\mathrm{.}5\%,$ the saving rate, $s,$ is $10\%,$ and the population growth rate, $n,$ is $7\mathrm{.}5\%.$

$($a$)$ What are the steady state levels of investment per worker, $i^{\text{'}\text{'}},$ output per worker, $y^{\text{'}\text{'}},$ and capital per worker, $k^{**},$ in this economy?

$($b$)$ Draw a graph of this economy; show the steady state levels of all variables that you calculated in part $($a$).$

$3$