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

Question 1

What is the 25^th term in the sequence: 5,7,9,11,13,15, ... .

Answer 1

53

Question 2

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?

Answer 2

620

Question 3

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?

Answer 3

35

Question 4

A population grows in a linear fashion. Suppose that the population begins (i.e. when N=0 ) with 500 individuals and after the tenth generation (i.e. when N=10 ), there are 1800 individuals. What is the value of the common difference d ?

Question 5

Given a sequence where find A₃₂ . Give your answer as a fraction in a reduced form.

Question 6

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?

Question 7

A geometric sequence has an initial term of 4 and a common ratio of 2. Use this information to find the sum of the first ten terms of this geometric sequence.

Question 8

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

Question 9

What is the next term in the sequence, 3,5,9,17,33,65,... .

Question 10

Given that A₁=17 and A₂=22 are the first two terms in an arithmetic sequence, find A₂₅ .

Question 11

Given that represent the term in sequence, then define a recursive
rule to be https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/. Find the value of .

Question 12

A geometric sequence has an initial term of 8 and a common ratio of 3 . Use this information to find the sum of the first twelve terms of this geometric sequence.

Question 13

A common sheet of copier paper is 0.1 mm in thickness. Each time the paper is folded in half; the total thickness is doubled. Suppose that you were able to fold the sheet of paper in half 25 times. What would be the thickness of this resulting paper mass?

Question 14

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 .

Question 15

Given that A₁=4 and A₂=5 , if A_N represents the N^th term in a sequence, then define a recursive rule to be
. Find the value of A₅ .

Question 16

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?

Question 17

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?

Question 18

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?

Question 19

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

Question 20

Given that A₅=7.5 and A₆=3.75 are the fifth and sixth terms in a geometric sequence, find A₁ .

Question 21

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) 89280
B) 92830
C) 109220
D) 123020
E) None of the above.

Question 22

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

A) 733
B) 756
C) 772
D) 789
E) None of the above.

Question 23

On the initial day of class (i.e. N=0 ), a professor counts 690 students as being present in her math class. On the 6^th day of class (i.e. N=5 ) the professor counts 450 students as being present in her math class. If the number of students decreases in a linear fashion, what is the common difference d ?

A) -6
B) -18
C) -36
D) -48
E) None of the above.

Question 24

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?

A)
B)
C)
D)
E) All of the above.

Question 25

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

A) 3645
B) 3789
C) 3945
D) 4135
E) None of the above.

Question 26

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) 4872
B) 5342
C) 6549
D) 7553
E) None of the above.

Question 27

On the initial day of class (i.e. N=0 ), a professor counts 480 students as being present in her math class. On the 11^th day of class (i.e. N=10 ) the professor counts 140 students as being present in her math class. If the number of students decreases in a linear fashion, what is the common difference d ?

A) -6
B) -18
C) -34
D) -48
E) None of the above.

Question 28

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 .

A) 17
B) 21
C) 23
D) 25
E) None of the above.

Question 29

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

A) 476
B) 498
C) 503
D) 523
E) None of the above.

Question 30

Jack is fascinated with sea-shells and he collects them every day on the beach. To start off with (i.e. when N=0 ), Jack has 45 sea-shells in his collection. Each day, Jack will add 14 sea-shells to his collection. After 49 days of adding shells, how many shells in total will Jack have?

A) 731
B) 745
C) 782
D) 815
E) None of the above.

Question 31

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) 5467
B) 6832
C) 7124
D) 8437
E) None of the above.

Question 32

Given that A₃=18 and A₅=2 are the 3^rd and 5^th terms in a geometric sequence, find A₁ .

A) 137
B) 143
C) 154
D) 162
E) None of the above.

Question 33

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?

A) 262144
B) 524288
C) 629145
D) 1048575
E) None of the above.

Question 34

Given that A₅=46 and A₇=60 are the 5^th and 7^th terms in an arithmetic sequence, find A₃₀ .

A) 176
B) 198
C) 221
D) 239
E) None of the above.

Question 35

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

A) 264
B) 273
C) 286
D) 298
E) None of the above.

Question 36

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 2^nd region you place 4 grains of rice, on the 3^rd regions you place 6 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?

A) 10
B) 682
C) 1364
D) 2541
E) None of the above.

Question 37

A geometric sequence has an initial term of 81920 and a common ratio of 0.5 . Based off of this information, what would be the sum of the first twelve terms of this geometric sequence?

A) 157900
B) 163800
C) 175400
D) 182500
E) None of the above.

Question 38

Given that A₁₁=35 Find the value of A₁₄ given

A) 234
B) 286
C) 308
D) 324
E) None of the above.

Question 39

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?

A) \operatorname{}
B)
C)
D)
E) None of the above.

Question 40

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) 2125
B) 2234
C) 2456
D) 2649
E) None of the above.