Decay Factor

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In 2011, USA Today reported the following:
Cleveland, Cincinnati, Toledo, Youngstown, Dayton, and Akron all suffered huge population declines from 2000 to 2010. Cleveland lost 17% of its population to fall to 396,815 - its fewest inhabitants since 1900.

a. What is the 10 year decay factor for the city of Cleveland? What does this 10 year decay factor tell you?

b. Assuming the population decayed exponentially, determine the 1 year decay factor and percent change of the city of Cleveland.

c. Write a function that gives the population of the city of Cleveland as a function of the number of years since 2010.

d. Assuming the population decayed exponentially, determine the 20 year decay factor and percent change of the city of Cleveland.

e. What does your model predict the population to be in 2015?

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@PaulaPolly,

a) The ten year decay factor is what you multiply the population by to get value ten years later. They already told you that the population dropped by 17%, so 83% of the population is left. That is the decay factor.

b) The ten year decay factor is equal to the one year decay factor to the 10th power, so X^10 = 0.83. The one year factor is 98.15%

c) The equation is the starting value times the decay factor to the time power, so 396,815*(0.9815)^n where n is the number of years since 2010.

d) The 20 year decay factor is going to be equal to the one year factor to the 20th power or the 10 year factor squared. 0.83^2 = 68.9%. The percent change in population is one minus that.

e) Just use the equation for question c

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Decay Factor

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