The population of a certain country is growing at 3.2 % per...

The population of a certain country is growing at $3.2 \%$ per year; that is, if it is $A$ at the beginning of a year, it is $1.032 A$ at the end of that year. Assuming that it is 4.5 million now, what will it be at the end of 1 year? 2 years? 10 years? 100 years?

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Key Concepts

Exponential Growth

Exponential growth describes the process where a quantity increases by a fixed percentage over equal time intervals, and as the quantity increases, the absolute amount added also increases. This type of growth is common in natural phenomena such as populations, where each successive period builds on the previous total.

Compound Growth Formula

The compound growth formula, typically written as A(t) = A0 * (1 + r)^t, is fundamental when calculating the future value of a quantity that grows at a constant rate each period. It demonstrates how repeated application of the growth rate leads to rapid accumulation over time.

Percentage Increase

Percentage increase involves augmenting a quantity by a certain percentage of its current value, converting the percentage to a decimal form for calculations. This concept is essential when applying repeated multiplicative increases to a base amount, as seen in scenarios like compound interest or exponential population growth.

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