MATH 110

1
MATH 110

• EXAM 4 Review

2
Arithmetic sequence
Geometric Sequence
Sum of an Arithmetic Series
Sum of a Finite Geometric Series
Sum of Infinite Geometric Series
3
Jeopardy
Leftovers!? Number Patterns Sumthing Two Steps Back Giant Leaps Forward Potent Potables
100 100 100 100 100 100
200 200 200 200 200 200
300 300 300 300 300 300
400 400 400 400 400 400
500 500 500 500 500 500
4
Leftovers !? 100

• A culture of bacteria originally numbers 500
  spores. After 2 hours there are 1500 bacteria.
  Assuming the number of spores can be modeled by
  the exponential function determine
  how many spores will be present in 6 hours.
• Answer 13,500 spores

5
Leftovers !? 200

• The cost of tuition at four-year public
  universities has been increasing roughly
  exponentially for the past several years. In
  1997, average tuition was 3,111 while in 2004 it
  was 5,132. Assuming that tuition will increase
  according to the exponential model ,
  at what rate is tuition increasing each year.
• Answer 7.41

6
Leftovers !? 300

• When rabbits were first brought to Australia,
  they multiplied very rapidly because there were
  no predators. In 1865, there were 60,000
  rabbits. By 1867, there 2,400,000 rabbits.
  Assuming exponential growth according to the
  model
• , when was the first pair of
  rabbits introduced into the country?
• Answer Around 1859

7
Leftovers !? 400

• The consumer price index compares the cost of
  goods and services over various years. The base
  year for comparison is 1967. The same goods and
  services that cost 100 in 1967 cost 184.50 in
  1977. Assuming that costs increase exponentially
  according to , when did the same
  goods and services cost double that of 1967?
• Answer 1978

8
Leftovers !? 500

• The proportion of carbon-14, an isotope of
  carbon, in living plant matter is constant. Once
  a plant dies, the carbon-14 in it begins to decay
  with a half-life of 5570 years. An archaeologist
  measures the remains of carbon-14 in a
  prehistoric hut and finds it to be one-tenth the
  amount of carbon-14 in the living wood. How old
  is the hut?
• Answer 18,503 years old

9
Number Patterns 100

• Consider the following sequence
• 7, 11, 15, 19, . . .
• Find the 150 term.
• Answer 603

10
Number Patterns 200

• How many terms are there in the following
  sequence
• Answer 25 terms

11
Number Patterns 300

• List the first four terms for the sequence whose
  formula is
• Answer 5, (1/5), 5, (1/5)

12
Number Patterns 400

• Consider the following sequence
• 375, -75, 15, -3, . . .
• What is the sign of the 493 term?
• Determine the most evident formula for the nth
  term of the sequence.
• Answer positive

13
Number Patterns 500

• Write a formula for the following sequence
• 1, 3, 6, 10, 15, . . .
• Answer

14
Sumthing 100

• Evaluate the expression
• Answer 66

15
Sumthing 200

• Re-index the following summation so that it
  starts at k 1

16
Sumthing 300

• It can be shown that the Euler number, e, can be
  approximated taking the square root of the
  following series
• Write this series using sigma notation.
• Answer

17
Sumthing 400

• Find the first term given that
  and
• Answer 25

18
Sumthing 500

• Find the value of the sum
• Answer 337,274

19
Two Steps Back 100

• Find the common difference of an arithmetic
  sequence whose 16th term is -73 and whose 21st
  term is -103.
• Answer -6

20
Two Steps Back 200

• Find the twentieth term of the arithmetic
  sequence whose third term is 6 and whose sixth
  term is 18.
• Answer 74

21
Two Steps Back 300

• Which of the following sequences is arithmetic?
• (I)
• (II)
• (III)

22
Two Steps Back 400

• Find the sum of the first 30 terms in an
  arithmetic sequence where the 6th term is 7 and
  the 12th term is 12.
• Answer 447.5

23
Two Steps Back 500

• Find the sum of all the numbers in the sequence
• Answer 18980

24
Giant Leaps Forward 100

• Find the common ratio of a geometric sequence
  where the 4th term is 100 and the 7th term is
  4/5.
• Answer 1/5

25
Giant Leaps Forward 200

• Find the first term of a geometric sequence whose
  fourth term is -8 and whose tenth term is
  -512/729.
• Answer -27

26
Giant Leaps Forward 300

• Which of the following sequences is geometric?
• (I)
• (II)
• (III)

27
Giant Leaps Forward 400

• Find the indicated sum
• Answer 56/3

28
Giant Leaps Forward 500

• A company plans to contribute to each of its
  employees retirement fund by depositing 100 at
  the end of each month in a retirement account.
  The account pays 6 interest compounded monthly.
  A look at the account balance shows that the
  amount is a series
• How much money will there be after 18 years
• Answer 38,929

29
Potent Potables 100

• Find the sum
• Answer 1661

30
Potent Potables 200

• Find the sum of the infinite geometric series if
  possible
• Answer Not possible

31
Potent Potables 300

• A repeating decimal can always be expressed as a
  fraction. Consider the decimal 0.23232323
  Use the fact that
• 0.23232323 0.23 0.0023 0.000023 .
• To write 0.232323 as a fraction.
• Answer 23/99

32
Potent Potables 400

• This problem illustrates how banks create credit
  and can lend out more money than has been
  deposited. Suppose that 100 is deposited in a
  bank. Experience shows that on average on 8 of
  the money deposited is withdrawn by the owner,
  which means that bank are free to lend 92 of
  their deposits. Thus, 92 of the original 100
  is loaned out to other customers. This 92 will
  become someone elses income, and eventually will
  be redeposited in the bank. So 92(0.92) 84.64
  is loaned out again and then redeposited, and so
  on. Find the total amount of money deposited in
  the bank.
• Answer 1250

33
Potent Potables 500

• Solve for x
• Answer 1/2