Question 712538
Let {{{L}}} = the number of lawyers and {{{P}}} = the population

given: {{{L = 100}}} and {{{P = 5000000}}}

At time {{{t}}} years after {{{1900}}}

{{{L = 100 * 2^(t/10)}}}.....if you do not see it good, here you have {{{2}}} to the power of {{{(t/10)}}}

{{{P = 5000000 + 200000t}}}

{{{20}}}% of the population = {{{(5000000 + 200000 t)(20/100)}}} = {{{(5000000 + 200000 t)*0.2}}}={{{1000000 + 40000t}}}

The year wanted is when

{{{100 * 2^(t/10) = 1000000 + 40000t}}}

{{{2^(t/10) = (1000000 + 40000t)/100}}}

{{{2^(t/10) = 10000 + 400t}}}

This is the required equation, you are not asked to solve it.