Mathematics in the modern World

1. Mathematics
In the
Modern
World
(Nature of
Mathematics
JASMIN C. TAWANTAWAN, LPT, Ph.D (CAR)

2. ◍ Pattern – are
regular,
repeated, or
recurring
forms or
designs.
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4. Nature forms of
pattern
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5. Roadmap
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1 3 5
6
4
2
Snowflakes and
Honeycombs
Tigers’ stripe and
hyenas’ Spots
Snail’s shell
Order of
rotation
Sunflower Flower petals
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World
population

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13. “
Formula of exponential growth:
𝑨 = 𝑷𝒆𝒓𝒕
Where,
A - is the size of the population
after in grows
P - is the initial number of people
r - is the rate of growth, and
t - is time
e – is Euler’s constant ≈ 𝟐. 𝟕𝟏𝟖
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14. This is a slide title
◍ Example:
The exponential growth model 𝐴 =
30𝑒0.02𝑡
describes the population of a
city in the Philippines in thousands, t
year after 1995.
a. What is the population of the city
in 1995?
b. What will be the population in 2017?
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15. ◍ Sequence – is an
order list of
numbers, called
terms, that may have
repeated values. The
arrangement of these
terms is set by
definite rule.
Sequence
Example: Analyze
the given sequence
for its rule and
identify the next
three terms.
a. 1, 10, 100, 1000
b. 2,5,9,14, 20
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16. Types of Number Patterns in Math
1. Arithmetic sequence
◍ An arithmetic sequence is
a sequence where every
term after the first is
obtained by adding a
constant called the
common difference.
In general the nth term of
a given sequence:
◍ 𝒂𝒏 = 𝒂𝟏 + 𝒏 − 𝟏
◍ 𝑺 =
𝒏
𝟐
(𝒂𝟏 + 𝒂𝒏)
◍ Example:
1. What is the 12th term
of the arithmetic
sequence 0, 5, 10, 15,
20, 25,…?
2. Find the sum of
arithmetic sequence 0,
5, 10, 15, 20, 25.
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17. 2. Geometric Sequence
◍ A geometric sequence is a
sequence where each term
after the first is
obtained by multiplying
the preceding term by a
nonzero constant called
the common ratio.
◍ 𝒂𝒏 = 𝒂𝟏
𝒓𝒏−𝟏.
◍ Example. Find
the common ratio
of the sequence
32, 16, 8, 4, 2,
... .
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18. 3. Fibonacci Sequence
The Fibonacci sequence
is defined by the
recursive formula
𝑭𝒏
= 𝑭𝒏−𝟐 + 𝑭𝒏−𝟏, 𝒘𝒉𝒆𝒓𝒆 𝑭𝟏
= 𝑭𝟐 = 𝟏
Example 1. Given the
recursive formula for the
Fibonacci sequence
𝐹𝑛 = 𝐹𝑛−2 + 𝐹𝑛−1,
𝑤ℎ𝑒𝑟𝑒 𝐹1 = 𝐹2 = 1.
a. 𝐹3
b. 𝐹4
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19. Mathematics for our world
◍ Mathematics
for
Organization
Ex. Sales,
internet, social
media, growth,
ideas, data, &
etc.
◍ Mathematics for
Prediction
Ex. Applying
concept of
probability,
historical
pattern,
metrological,
weather, & etc.
◍ Mathematics
for Control
Ex.
Gravitational
waves, threat
of climate
change
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20. Thanks!
Any questions?
👍
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Activity 1
Determine what comes next in the given pattern.
1. A, C, E, G, I, ______
2. 15, 10, 14, 10, 13, 10, ____
3. 3,6,12,24,48,96,____
4. 27,30,33,36,39,_____
5. 41,30,37,35,33,____
Find the missing quantity.
1. 𝑃 = 680,000; 𝑟 = 12% 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟; 𝑡 = 8 𝑦𝑒𝑎𝑟𝑠
2. 𝐴 = 1,240,000; 𝑟 = 8% 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟; 𝑡 = 30 𝑦𝑒𝑎𝑟𝑠