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Diseases tend to spread according to the exponential growth model. In the early days of AIDS,...

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Advance Math

  1. Diseases tend to spread according to the exponential growthmodel. In the early days of AIDS, the growth factor (i.e. commonratio; growth multiplier) was around 2.1. In 1983, about 1800people in the U.S. died of AIDS. If the trend had continuedunchecked, how many people would have died from AIDS in 2005?

   ______________________people

(Note: once diseases become widespread, they start to behavemore like logistic growth, but don't worry about that for thepurpose of this exercise)

2 . A population grows according to an exponential growth model.The initial population is P0=10, and the growth rate is r=0.45.

Then:

P1 =

P2 =

Find an explicit formula for Pn. Your formula should involven.

Pn =   

Use your formula to find P12

P12 =

Give all answers accurate to at least one decimal place

3 . Assume there is a certain population of fish in a pond whosegrowth is described by the logistic equation. It is estimated thatthe carrying capacity for the pond is 1800 fish. Absentconstraints, the population would grow by 240% per year.

If the starting population is given by p0=500, then after onebreeding season the population of the pond is given by

p1 =   

After two breeding seasons the population of the pond is givenby

p2 =   

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