SOLUTION: Hi, I'm Allen and I asked for assistance with this problem earlier but got no response (I don't know why questions go unanswered sometimes). Anyways, here it is again: In the ye

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hi, I'm Allen and I asked for assistance with this problem earlier but got no response (I don't know why questions go unanswered sometimes). Anyways, here it is again: In the ye      Log On


   

Question 712538: Hi, I'm Allen and I asked for assistance with this problem earlier but got no response (I don't know why questions go unanswered sometimes). Anyways, here it is again:
In the year 1900, in the country Acirema, there were 100 Lawyers and 5 million people. Every 10 years, the number of Lawyers doubles, and the population increases by 2 million. Let t be the number of years after 1900. Thus t=3 corresponds to 1903. Find the equation involving t whose solution tells you in which year 20 percent of the population are Lawyers. DO NOT SOLVE OR BEGIN TO SOLVE THIS EQUATION.
.2 = ____________
Thanks in advance!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Let L = the number of lawyers and P = the population
given: L+=+100 and P+=+5000000
At time t years after 1900
L+=+100+%2A+2%5E%28t%2F10%29.....if you do not see it good, here you have 2 to the power of %28t%2F10%29
P+=+5000000+%2B+200000t
20% of the population = %285000000+%2B+200000+t%29%2820%2F100%29 = %285000000+%2B+200000+t%29%2A0.2=1000000+%2B+40000t
The year wanted is when
100+%2A+2%5E%28t%2F10%29+=+1000000+%2B+40000t
2%5E%28t%2F10%29+=+%281000000+%2B+40000t%29%2F100
2%5E%28t%2F10%29+=+10000+%2B+400t
This is the required equation, you are not asked to solve it.