The population of an Atlanta suburb is growing at a rate of...

The population of an Atlanta suburb is growing at a rate of 3.6\% per year. If 21,000 people lived in the suburb in 2004 , determine how many people will live in the town in $2012 .$ Use $y=y_{0} e^{0.036 t}$

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Key Concepts

Initial Value

The initial value, denoted by y? in the exponential growth formula, represents the starting quantity at time t = 0. It serves as the baseline for calculating future values as the process of exponential growth continues.

Time Interval Interpretation

In the context of exponential growth, correctly determining the time interval (t) is crucial. This involves calculating the difference between the initial time and the target time, ensuring that the growth rate is applied over the correct period.

Exponential Growth

Exponential growth refers to a process where the quantity increases at a rate proportional to its current value. In contexts like population dynamics, this means that as the population grows, the absolute increase per time unit becomes larger, leading to faster overall growth over time.

Continuous Exponential Growth Formula

The continuous exponential growth formula is given by y = y?e^(rt), where y? is the initial amount, r is the continuous growth rate, and t is time. This formula is used to model processes that grow continuously rather than in discrete steps, accurately representing constant percentage growth over time.

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