In the year 1900, in the country Acirema, there were 100 Lawyers and 2 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=___________________?????

Question

20-02-2014
Mathematics

Answered

In the year 1900, in the country Acirema, there were 100 Lawyers and 2 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=___________________?????

Verified Answer :

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Anonymous Anonymous · Answer 1 · 2014-02-21T03:03:29-05:00

Anonymous Anonymous

21-02-2014

Well, there is a system:
\(L=100*2^{\frac{t}{10}}\)
\(p=2000000+2000000*\frac{t}{10}\)
\(L=.2P\)
I'd guess you need the last equation in a different form: \(.2=\frac{L}{P}\)

Answer Link

AkshayG AkshayG · Answer 2 · 2019-11-14T06:58:12-05:00

The equation is \(\boxed{0.2 = \frac{{100 \times {2^{\dfrac{t}{{10}}}}}}{{2000000 + 2000000 \times \dfrac{t}{{10}}}}}.\)

Further explanation:

Explanation:

In the year 1900 the population of the country is 2 million.

The number of lawyers in 1900 is 100.

Every 10 years the number of lawyers doubles and the population increases by 2 million.

Consider number of the lawyer as \(x\) and the population of the country as \(y\).

The expression of increasing the number of lawyers can be expressed as follows,

\(x = 100 \times {2^{\dfrac{t}{{10}}}}\)

The population of the country can be expressed as follows,

\(y = 2000000 + 2000000 \times \dfrac{t}{{10}}\)

20 percent of the populations are Lawyers.

\(\begin{aligned}0.2y&= x\\0.2&= \frac{x}{y}\\0.2&= \frac{{100 \times {2^{\frac{t}{{10}}}}}}{{2000000\left( {1 + \frac{t}{{10}}} \right)}}\\\end{aligned}\)

The equation is \(\boxed{0.2 = \dfrac{{100 \times {2^{\dfrac{t}{{10}}}}}}{{2000000 + 2000000 \times \dfrac{t}{{10}}}}}.\)

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Exponential equation

Keywords: lawyers, in the year 1900, 100 lawyers, 2 million people, 10 years, Country, Acirema, lawyers double, population increase by 2 million, t, number of years, 1903, equation, involving t, solution, 20 percent population are laywers.