1.Consider a population that grows according to the recursive rulePn=Pn1+95Pn=Pn-1+95, with initial populationP0=40P0=40.

Then:

P1P1=

P2P2=

Find an explicit formula for the population. Your formula should involvenn(use lowercase n)

Pn=Pn=

Use your explicit formula to findP100P100

P100P100=

2.A population of beetles are growing according to a linear growth model. The initial population (week 0) isP0=9P0=9, and the population after 5 weeks isP5=29P5=29.

Find an explicit formula for the beetle population afternnweeks.

PnPn=

After how many weeks will the beetle population reach 117?

___________weeks

3.A city currently has 132 streetlights. As part of a urban renewal program, the city council has decided to install 3 additional streetlights at the end of each week for the next 52 weeks.

How many streetlights will the city have at the end of 49 weeks?

____________________streetlights

4.A population grows according to an exponential growth model. The initial population isP0=10P0=10, and the growth rate isr=0.3r=0.3.

Then:

P1P1=

P2P2=

Find an explicit formula forPnPn. Your formula should involvenn.

PnPn=

Use your formula to findP12P12

P12P12=

Give all answers accurate to at least one decimal place

5.A population grows according to an exponential growth model, withP0=40P0=40andP1=44P1=44

Complete the recursive formula:

PnPn=Pn1Pn-1

Write a explicit formula forPnPn

PnPn=

6.Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 2.0. In 1983, about 1500 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2005?

____________people

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

7.Tacoma's population in 2000 was about 200 thousand, and has been growing by about 8% each year. If this continues, what will Tacoma's population be in 2010?

___________people

8.Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 2% each year. In other words, if you have $1 this year, next year it will only buy you $0.98 worth of stuff. How much will $100 buy you in 20 years?

$_________

9.Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1800 fish. Absent constraints, the population would grow by 230% per year.

If the starting population is given byp0=200p0=200, then after one breeding season the population of the pond is given by

p1p1=

After two breeding seasons the population of the pond is given by

p2p2=

10.Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 1.9. In 1983, about 1600 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2006?

__________people

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

11.Tacoma's population in 2000 was about 200 thousand, and has been growing by about 8% each year. If this continues, what will Tacoma's population be in 2015?

____________thousand people

12.Consider a population that grows according to the recursive rulePn=Pn1+115Pn=Pn-1+115, with initial populationP0=20P0=20.

Then:

P1P1=

P2P2=

Find an explicit formula for the population. Your formula should involvenn(use lowercase n)

Pn=Pn=

Use your explicit formula to findP100P100

P100P100=

13.A city currently has 136 streetlights. As part of a urban renewal program, the city council has decided to install 3 additional streetlights at the end of each week for the next 52 weeks.

How many streetlights will the city have at the end of 32 weeks?

____________streetlights

14.A population grows according to an exponential growth model. The initial population isP0=3P0=3, and the common ratio isr=1.4r=1.4.

Then:

P1P1=

P2P2=

Find an explicit formula forPnPn. Your formula should involvenn.

PnPn=

Use your formula to findP11P11

P11P11=