Approximately 160 billion text messages were sent worldwide...

Approximately 160 billion text messages were sent worldwide in 2000 . Since then, the number of text messages sent each year has grow by about $33 \%$ per year. How many text messages were sent worldwide from 2000 through $2010 ?$

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Key Concepts

Compound Growth

Compound growth, similar to compound interest, refers to a growth process where each period's increase is added to the principal amount, and future growth is calculated on the new total. This concept is key in understanding accumulative processes where the base for growth increases over time.

Geometric Series

A geometric series is the sum of the terms of a geometric sequence. It is useful for calculating the total accumulated value over multiple periods of exponential growth, allowing one to sum contributions from each period to determine an overall total.

Exponential Growth

Exponential growth occurs when the rate of increase of a quantity is proportional to its current value, leading to a rapid rise over time. This concept is fundamental in many areas, including finance, population studies, and natural processes, where growth compounds on top of previous increases.

Geometric Sequence

A geometric sequence is a series of numbers in which each term is obtained by multiplying the previous term by a constant factor, known as the common ratio. This concept models scenarios where quantities increase or decrease by a constant percentage over discrete time intervals.

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