With Shaking Hands
KERJA PROJEK MATEMATIK TAMBAHAN 2013
NAMA: MUHAMMAD HASSANAL HAIKAL BIN HAYAT
KELAS: 5 ABU BAKAR (2013)
NO. I.C.: 961029-13-5199
NAMA GURU: PUAN SHARINA BINTI MOHD. ZULKIFLI
INTRODUCTION
Exponential growth describes a process of a value increasing by multiplication of itself and then increasing by multiplication of the product.
Below is an example the value 2 increasing exponentially over 4 stages:
2 * 2 = 4
4 * 4 = 16
16 * 16 = 96
96 * 96 = 9216
Exponential growth occurs when the growth rate of the value of a mathematical function is proportional to the function's current value. Exponential decay occurs in the same way when the growth rate is negative. In the case of a discrete domain of definition with equal intervals it is also called geometric growth or geometric decay (the function values form a geometric progression). The exponential growth model is also known as the Malthusian growth model.
The formula for exponential growth of a variable x at the (positive or negative) growth rate r, as time t goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is
where x0 is the value of x at time 0. For example, with a growth rate of r = 5% = 0.05, going from any integer value of time to the next integer causes x at the second time to be 1.05 times (i.e., 5% larger than) what it was at the previous time.
TASK 1
a)T11= 25(2)11-1 = 25600 rabbits
b) i) 7 years: 14 months= Doubled 14 times ii) T15= 25(2)15-1 = 409600 rabbits
c) T11= 25(3)11-1 = 1476225 rabbits
d) T12= 25(2)12-1 = 51200 rabbits
TASK 2
a)
Year | Number of rabbits | 2009 | 25 | 2010 | 50 | 2011 | 100 | 2012 | 200 | 2013 | 400 | 2014 | 800 | 2015 | 1600 | 2016 | 3200 | 2017 | 6400 | 2018 | 12800 | 2019 | 25600 | 2020 | 51200 |
b) Year | Population | 1940 | 4475000 | 1950 | 6110000 | 1960 | 8160000 | 1970 | 10910000 | 1980 | 13830000 | 1990 | 18210000 | 2000 | 23410000 |
c) x | b | y | 0 | 0 | 4475000
NAMA: MUHAMMAD HASSANAL HAIKAL BIN HAYAT
KELAS: 5 ABU BAKAR (2013)
NO. I.C.: 961029-13-5199
NAMA GURU: PUAN SHARINA BINTI MOHD. ZULKIFLI
INTRODUCTION
Exponential growth describes a process of a value increasing by multiplication of itself and then increasing by multiplication of the product.
Below is an example the value 2 increasing exponentially over 4 stages:
2 * 2 = 4
4 * 4 = 16
16 * 16 = 96
96 * 96 = 9216
Exponential growth occurs when the growth rate of the value of a mathematical function is proportional to the function's current value. Exponential decay occurs in the same way when the growth rate is negative. In the case of a discrete domain of definition with equal intervals it is also called geometric growth or geometric decay (the function values form a geometric progression). The exponential growth model is also known as the Malthusian growth model.
The formula for exponential growth of a variable x at the (positive or negative) growth rate r, as time t goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is
where x0 is the value of x at time 0. For example, with a growth rate of r = 5% = 0.05, going from any integer value of time to the next integer causes x at the second time to be 1.05 times (i.e., 5% larger than) what it was at the previous time.
TASK 1
a)T11= 25(2)11-1 = 25600 rabbits
b) i) 7 years: 14 months= Doubled 14 times ii) T15= 25(2)15-1 = 409600 rabbits
c) T11= 25(3)11-1 = 1476225 rabbits
d) T12= 25(2)12-1 = 51200 rabbits
TASK 2
a)
Year | Number of rabbits | 2009 | 25 | 2010 | 50 | 2011 | 100 | 2012 | 200 | 2013 | 400 | 2014 | 800 | 2015 | 1600 | 2016 | 3200 | 2017 | 6400 | 2018 | 12800 | 2019 | 25600 | 2020 | 51200 |
b) Year | Population | 1940 | 4475000 | 1950 | 6110000 | 1960 | 8160000 | 1970 | 10910000 | 1980 | 13830000 | 1990 | 18210000 | 2000 | 23410000 |
c) x | b | y | 0 | 0 | 4475000