Question

Country A has a growth rate of 2.2% per year. The population is currently 5,667,000, and the land area of Country A is 31,000,000,000 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

It will be 290 years until there be one person for every square yard of land.

Explanation:

We are looking for when the country's population is equivalent to its area in square yards: 31,000,000,000.

Write an equation for the situation: (Trickiest part)

p(x) = (5,667,000)(1 + 0.022)ˣ <= Can modify compound interest equation

31,000,000,000 = (5,667,000)(1 .022ˣ)

Started rounding off numbers

547.056 = 1 .022ˣ <=
`x = (log(ans))/(log(base))`

Solve using log.

x = 2.738 / 0.00945 <= log(547.056) / log(1.022)

x = 289.7 <= Round up because rate is annual. Before the 290th year, the population is less than the number of square yards.

x = 290

Total amount with annual compound interest equation applied to this problem:

`A = P(1 + r)^(t)` (Principle is starting investment)

Population = (Starting population)(1 + growth rate)^(time)