Exam 9: Population Growth Models: There Is Strength in Numbers

A large office building has a capacity of 12,000 people and currently 800 have heard a juicy rumor. Assuming that the rumor spreads according to a logistic model with a growth rate of r = 4.0, how many people does the logistic growth model predict to have heard the rumor after three transitions?

A circular game board is shown below. The board consists of ten different regions. Half of the regions are black and half of the regions are white. Suppose that you start on one of the white regions and you move around the board clockwise. On the first region you place 2 grains of rice, on the 2nd region you place 4 grains of rice, on the 3rd regions you place 8 grains of rice, and so on following the pattern. You stop placing grains of rice after you reach the 10th region. What would be the difference between the total number of grains found on white regions and the total number of grains found on black regions?

Given a sequence where find A₂₄ . Give your answer as a fraction in reduced form.

Given that A₂₃=89 , find the value of A₂₆ given

Given that A₂=35 and A₃=41 are the 2^nd and 3^rd terms an arithmetic sequence, find the term number N such that A_N=149 .

Given that A₂=45 and A₃=135 are the 2^nd and 3^rd terms in a geometric sequence, find A₆ .

What is the 100^th term of the sequence 1,4,7,10,13,16,..... ?

Mary is fascinated with rocks and she collects them every day at the park. To start off with (i.e. when N=0 ), Mary has 32 rocks in her collection. Each day, Mary will add 12 new rocks to her collection. After 49 days of adding rocks, how many rocks in total will Mary have?

Jack is fascinated with sea-shells and he collects them every day on the beach. To start off with , Jack has 25 sea-shells in his collection. Each day, Jack will add 8 sea-shells to his collection. After 99 days of adding shells, how many shells in total will Jack have?

A large office building has a capacity of 15,000 people and currently 1,000 have had contact with a nasty cold virus. Assuming that the virus spreads according to a logistic model with a growth rate of r =3.0 , how many people does the logistic growth model predict to have come into contact with the virus after two transitions?

A circular game board is shown below. The board consists of ten different regions. Half of the regions are black and half of the regions are white. Suppose that you start on one of the white regions and you move around the board clockwise. On the first region you place 3 grains of rice, on the 2^nd region you place 12 grains of rice, on the 3^rd regions you place 48 grains of rice, and so on following the pattern. You stop placing grains of rice after you reach the 10^th region. What would be the difference between the total number of grains found on white regions and the total number of grains found on black regions?

Given that A₁=13 and A₂=17 are the first two terms in an arithmetic sequence, find the term number N such that A_N=145 .

A large office building has a capacity of 14,000 people and currently 1200 have heard a juicy rumor. Assuming that the rumor spreads according to a logistic model with a growth rate of r=3.0 , how many people does the logistic growth model predict to have heard the rumor after two transitions?

A population grows in a linear fashion. Suppose that the population begins , there are 240 individuals. What is the value of the common difference d?

Given that A₃=24 and A₅=96 are the third and fifth terms in a geometric sequence, find A₁₅ .

Mary is fascinated with rocks and she collects them every day at the park. To start off with (i.e. when N=0 ), Mary has 46 rocks in her collection. Each day, Mary will add 21 new rocks to her collection. After 99 days of adding rocks, how many rocks in total will Mary have?

A geometric sequence has an initial term of 81920 and a common ratio of 0.25 . Based off of this information, what would be the sum of the first seven terms of this geometric sequence?

A large office building has a capacity of 10,000 people and currently 500 have had contact with a nasty cold virus. Assuming that the virus spreads according to a logistic model with a growth rate of r = 2.0, how many people does the logistic growth model predict to have come into contact with the virus after three transitions?

If A_N represents the N^th term of a sequence, then define a recursive rule as Which of the following equations is a restatement of this rule?

What is the 100^th term of the sequence 3,8,13,18,23,28,..... ?