Exponential Growth And Decay Worksheets

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Exponential Growth And Decay Worksheets
Exponential Growth And Decay Worksheets
Exponential growth and decay are the types of models by which we measures the function's
value either it is increasing or decreasing at a given time. The exponential can be expressed
in terms of the designated power of e. that is natural logarithm base. The simple means of
exponential growth is, when some volume or accumulation continuously increases with a
certain percentage. The wel known and very popular example of exponential growth is the
population of any country when it increases.
If there is a growth in any quantity's value then the growth rate should be directly proportional
to that quantity's value.
To calculate the exponential growth, below we have a exponential growth formula: -
N (t) = N0 e t
Where N is the quantity.
t is the parameter.


is the constant.
Ex is the exponential function
and N 0 is the initial value.
The exponential growth model is also cal ed the Malthusian model.
The most popular example of exponential growth is population growth, so let's take the
example of population growth to understand the exponential growth.
An economic expert is analyzing the population growth in any country. He calculated that 100,
00, 00 people are present at the time of initial estimation, and after one hour the population
has just tripled. On this bases we can make an equation like s(t) = 100,00,00ekt where k
defining the fact that population is tripled in one hour that means after one hour population =
3* population before one hour. It can also be represented as k = l n(3).
So new equation s(t) = 100,00,00(3)t. So on the basis this equation anyone can easily predict
the population after one hour, two hour, three hour, four hour and so on. Where t denotes the
number of hours. According to this equation population after six hour wil be s(6) =
The exponential decay is the concept of the exponential growth. It is the reverse of the
exponential growth. As the name of exponential decay implies that when some volume or
accumulation continuously decreases with a certain percentage. The equation of the
exponential decay can be expressed as below: - N(t) = -N0 e - kt
Example of exponential decay is: - Suppose, on Friday any restaurant have 4000 customers.
On Saturday morning, local news paper publishes that this restaurant uses unhygienic
materials to make the dishes, then that day that restaurant serves 2000 customers, and on
Sunday, that restaurant serves 1000 customers and on Monday the restaurant serves the 500
customers so day by day the customer population is decreasing means exponential decay.


In the above example the customer population is decreasing 50 percent everyday. This is the
type that is total y differs from the linear function. In a linear function the customer population
wil be decrease by the same amount every day. It means in a linear function the degradation
processes wil be like this
Friday : - 4000
Saturday : - 3000
Sunday : - 2000
Monday :- 1000
But it is not like this in exponential decay. We can also use this formula y = a(1-b)x to
calculate exponential decay.

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