9.6 EXPONENTIAL GROWTH AND DECAY. EQUATIONS THAT DEAL WITH E Continuously Compounded Interest A=Pe rt A= amount in account after t years t= # of years.

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Presentation transcript:

9.6 EXPONENTIAL GROWTH AND DECAY

EQUATIONS THAT DEAL WITH E Continuously Compounded Interest A=Pe rt A= amount in account after t years t= # of years r= annual interest rate P= amount of principal invested

EXAMPLES Suppose you deposit $1000 in an account paying 2.5% annual interest, compounded continuously.  Find the balance after 10 years  Find how long it will take for the balance to reach at least $1500

Suppose you deposit $5000 in an account paying 3% annual interst, compounded continuously.  Find what the balance would be after 5 years  Find how long it will take for the balance to reach at least $7000

EXPONENTIAL DECAY y=a(1-r) t a=initial amount r=% of decrease expressed as a decimal, this is also called rate of decay t=time y=ae -kt a=initial amount k=constant t=time

EXAMPLE 3 A cup of coffee contains 130 milligrams of caffeine. If caffeine is eliminated from the body at a rate of 11% per hour, how long will it take for half of this caffeine to be eliminated?

EXAMPLE 4 The half-life of Sodium-22 is 2.6 years.  What is the value of k and the equation of decay for Sodium-22?  A geologist examining a meteorite estimates that it contains only about 10% as much Sodium-22 as it would have contained when it reached Earth’s surface. How long ago did the meteorite reach Earth?

EXPONENTIAL GROWTH y=a(1+r) t a= initial amount r=% of increase/growth expressed as a decimal t=time y=ae kt a=initial amount k=constant t=time

EXAMPLE 5 Home values in Millersport increase about 4% per year. Mr. Thomas purchased his home eight years ago for $122,000. What is the value of his home now?

EXAMPLE 6 The population of a city of one million is increasing at a rate of 3% per year. If the population continues to grow at this rate, in how many years will the population have doubled?

EXAMPLE 7 Two different types of bacteria in two different cultures reproduce exponentially. The first type can be modeled by B 1 (t)=1200e t and the second can be modeled B 2 (t)=3000e t where t is the number of hours. According to these models, how many hours will it take for the amount of B 1 to exceed the amount of B 2 ?