Question

Country A has a growth rate of 4.9​% per year. The population is currently 4 comma 151​,000, and the land area of Country A is 14​,000,000,000 square yards. Assuming this growth rate continues and is​ exponential, after how long will there be one person for every square yard of​ land?

Answer 1

There will be one person on 1 square yard of land after 1,892,147.588 years.

Explanation:

Continuous exponential growth formula:

`P(t)=Pe^(rt)`

P(t)= Population after t years.

P= Initial population

r=rate of growth.

t= time in year

Given that,

Growth rate of country A (r)= 4.9% per year=0.049 per year.

Initial population (P)= 151,000.

Land area of country area= 14,000,000,000 square yards.

There will be one person on one square yard of land.

So, there will be 14,000,000,000 person for 14,000,000,000 square yard of land in country A.

P(t)=14,000,000,000 person

`\therefore 14,000,000,000= 151,000 e^(0.049t)`

`\Rightarrow e^(0.049t)=( 14,000,000,000)/( 151,000)`

Taking ln both sides

`\Rightarrow ln|e^(0.049t)|=ln|( 14,000,000,000)/( 151,000)|`

`\Rightarrow {0.049t}=ln|( 14,000,000,000)/( 151,000)|`

`\Rightarrow t}=(ln|( 14,000,000,000)/( 151,000)|)/(0.049)`

`\Rightarrow t}=1,892,147.588` years

There will be one person for every square yard of land after 1,892,147.588 years.