The exponential models describe the population of the...

The exponential models describe the population of the indicated country, $A,$ in millions, t years after $2010 .$
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Which countries have a decreasing population? By what percentage is the population of these countries decreasing each year?

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Key Concepts

Exponential Functions

Exponential functions describe processes where a quantity changes at a rate proportional to its current value. In the context of population models, they are typically written as P(t) = P? · b?, where P? is the initial population and b is the constant growth (if b > 1) or decay (if b < 1) factor.

Exponential Decay

Exponential decay occurs when the base of the exponential function is less than 1. This indicates that the quantity decreases over time by a constant multiplicative rate, which can be converted into a yearly percentage decrease using the formula (1 - b) × 100%.

Population Modeling

Population modeling uses exponential functions to reflect how populations change over time. By examining the base parameter in these models, one can determine if the population is increasing (growth) or decreasing (decay) and quantify the rate of change annually.

Interpreting Percentage Change

The percentage change in an exponential model is derived directly from the base. For a base less than 1, subtracting the base from 1 and then multiplying by 100 yields the percentage decrease per time unit, indicating how rapidly the population is declining.

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