
How to calculate the exponential growth factor?
Answer
484.8k+ views
Hint: The exponential growth factor represents the exponential increase in the growth of a quantity with respect to time; we will see the steps and the example of finding the exponential growth factor. Finally we conclude the required answer.
Complete step-by-step solution:
The exponential growth can be calculated using the following steps:
Step : We have to determine the initial or the present value for the quantity we want to find the future value.
Step : Try to determine the growth rate of that quantity, it can be in terms of years or months to even minutes and seconds.
Step : now the tenure or the total period for which the quantity will stay in the system has to be figured out.
Step : now the total number of periods in the tenure have to be calculated for which the growth has to be compounded and calculated.
Step : Finally, the exponential growth will be calculated by compounding the initial value, the annual growth rate and the number of periods in the tenure.
Now let’s consider an example of a doubling life of a quantity:
Now exponential growth is generally represented by the formula: .
Where is the value of the quantity at time and is the exponential growth factor and is the initial value.
Now to find the value of , we need another equation given.
Let’s consider the doubling life of the quantity be years, therefore:
.
Now on cancelling from both the sides we get:
On taking log to the base on both the sides, we get:
Now on simplifying we get:
Now we know that , therefore we get:
Thus,
Now on using a scientific calculator we get:
Which is the value of which is the exponential growth factor or the constant.
Note: Exponential growth and decay is used in the science fields to predict what will be the state of a quantity in the future, a quantity would increase which is called growth, or a quantity can decrease which is called decay.
Complete step-by-step solution:
The exponential growth can be calculated using the following steps:
Step
Step
Step
Step
Step
Now let’s consider an example of a doubling life of a quantity:
Now exponential growth is generally represented by the formula:
Where
Now to find the value of
Let’s consider the doubling life of the quantity be
Now on cancelling
On taking log to the base
Now on simplifying we get:
Now we know that
Thus,
Now on using a scientific calculator we get:
Which is the value of
Note: Exponential growth and decay is used in the science fields to predict what will be the state of a quantity in the future, a quantity would increase which is called growth, or a quantity can decrease which is called decay.
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