## Answer :

[tex]L=100*2^{\frac{t}{10}}[/tex]

[tex]p=2000000+2000000*\frac{t}{10}[/tex]

[tex]L=.2P[/tex]

I'd guess you need the last equation in a different form: [tex].2=\frac{L}{P}[/tex]

The equation is [tex]\boxed{0.2 = \frac{{100 \times {2^{\dfrac{t}{{10}}}}}}{{2000000 + 2000000 \times \dfrac{t}{{10}}}}}.[/tex]

**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 [tex]x[/tex] and the population of the country as [tex]y[/tex].

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

[tex]x = 100 \times {2^{\dfrac{t}{{10}}}}[/tex]

The population of the country can be expressed as follows,

[tex]y = 2000000 + 2000000 \times \dfrac{t}{{10}}[/tex]

20 percent of the populations are Lawyers.

[tex]\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}[/tex]

The equation is [tex]\boxed{0.2 = \dfrac{{100 \times {2^{\dfrac{t}{{10}}}}}}{{2000000 + 2000000 \times \dfrac{t}{{10}}}}}.[/tex]

**Learn more:
**

**1. **Learn more about inverse of the functionhttps://brainly.com/question/1632445.

**2.** Learn more about equation of circle brainly.com/question/1506955.

**3.** Learn more about range and domain of the function https://brainly.com/question/3412497

**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.