EXPONENTIAL GROWTH AND DECAY Review of Vocabulary Variables

EXPONENTIAL GROWTH AND DECAY

Review of Vocabulary & Variables • a: initial -or- original amount • b: 1 + r -or- 1 - r • r: growth rate • x: time • appreciate: when an object gains value; grows exponentially • depreciate: when an object looses value; decays exponentially • half-life: the amount of time it takes for half of the amount of a substance to decay

Exponential Growth … … occurs when a quantity INCREASES by the same rate in each time period. Equation for Exponential Growth: y = abx y = final amount a = original –or- initial amount b = 1 + r (written as a decimal) r = rate (change to a decimal) x = time

Exponential Decay … … occurs when a quantity DECREASES by the same rate in each time period. Equation for Exponential Decay: y = abx y = final amount a = original –or- initial amount b = 1 - r (written as a decimal) r = rate (change to a decimal) x = time

Example 1… The original value of a painting is $1400, and the value increases by 9% each year. Write a function to model this situation then find the value of the painting in 25 years. Function: y= a= r= b= t= Value:

Your Turn to Try … A sculpture is increasing in value at a rate of 8% per year, and its value in 2000 was $1200. Write a function to model this situation then find the sculptures value in 2006. Function: y= a= r= b= t= Value:

Example 2 … The population of a town is decreasing at a rate of 1% per year. In 2000, there were 1300 people. Write a function to model this situation and find the population in 2008. Function: y= a= r= b= t= Value:

It’s Your Turn Again … The fish population in a local stream is decreasing at a rate of 3% per year. The original population was 48, 000. Write a function to model this situation then find the population after 7 years. Function: y= a= r= b= t= Value:

Example 3 … Technetium-99 m is a radioactive substance used to diagnose brain, thyroid, liver, and kidney diseases. The half-life of technetium-99 m is 6 hours. If there are 200 mg of technetium-99 m, how much will there be in 24 hours?

Your Turn … The half-life of radium-226 is 1620 years. If there are currently 1504 g of radium-226 at a toxic waste dump, how long will it be before there are only 100 g remaining?