Consider the Following Romer Model of Economic Growth (A) If $A _ { 0 } = 100 , \bar { \ell } = 0.1 , \bar { z } = 1 / 3000$

Consider the following Romer model of economic growth: $\begin{array} { l } Y _ { t } = A _ { t } L _ { y t } \\\Delta A _ { t } = \bar { z } A _ { t } L _ { t } \\L _ { a t } + L _ { y t } = \bar { L } \\L _ { u t } = \bar { \ell } \bar { L }\end{array}$
(a) If $A _ { 0 } = 100 , \bar { \ell } = 0.1 , \bar { z } = 1 / 3000$
and $\bar { L } = 1,000$

, what is the growth rate of knowledge in this economy?
(b)What is the growth rate of per capita output in this economy?
(c) Using the information from year 1, what is the level of per capita output in this economy in year 5?