# With Shaking Hands

Topics: Exponential growth, Exponential function, Exponentiation Pages: 4 (772 words) Published: June 20, 2013
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.

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

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|...