Exponential Growth and Decay Functions Section 12.4 Exponential Growth and Decay Functions

Exponential Growth/Decay A quantity that grows or decays by the same percent at regular time periods is said to have exponential growth or exponential decay. There are many real-life examples of exponential growth and decay, such as population, bacteria, viruses, and radioactive substances, just to name a few.

Graphs of Exponential Functions y We would find a pattern in the graphs of all the exponential functions of the type bx, where b > 1. This models exponential growth.

Graphs of Exponential Functions y We would find a pattern in the graphs of all the exponential functions of the type bx, where 0 < b < 1. This models exponential decay.

Exponential Growth and Decay A quantity that grows or decays by the same percent at regular time periods is said to have exponential growth or exponential decay. Exponential Growth initial amount number of time intervals (1 + r) is the growth factor r is the growth rate as a decimal

Example In 2005, let’s suppose a town named Jackson had a population of 15,500 and was consistently increasing by 10% per year. If this yearly increase continues, predict the city’s population in 2025. (Round to the nearest whole.)

Exponential Growth and Decay A quantity that grows or decays by the same percent at regular time periods is said to have exponential growth or exponential decay. Exponential Decay initial amount number of time intervals (1 ‒ r) is the decay factor r is the decay rate (often a percent)

Example A large golf country club holds a singles tournament each year. At the start of the tournament for a particular year there are 512 players. After each round, half the players are eliminated. How many players remain after 6 rounds?