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 well 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 λ t Where N is the quantity. t is the parameter.
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λ is the constant. Ex is the exponential function and N 0 is the initial value. The exponential growth model is also called 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 will be s(6) = 100,00,00(3)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.
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In the above example the customer population is decreasing 50 percent everyday. This is the type that is totally differs from the linear function. In a linear function the customer population will be decrease by the same amount every day. It means in a linear function the degradation processes will 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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