Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

How to calculate the exponential growth factor?

Answer
VerifiedVerified
479.7k+ views
like imagedislike image
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 1: We have to determine the initial or the present value for the quantity we want to find the future value.
Step 2: Try to determine the growth rate of that quantity, it can be in terms of years or months to even minutes and seconds.
Step 3: now the tenure or the total period for which the quantity will stay in the system has to be figured out.
Step 4: now the total number of periods in the tenure have to be calculated for which the growth has to be compounded and calculated.
Step 5: 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: P(t)=P0ekt.
Where P(t) is the value of the quantity at time t and k is the exponential growth factor and P0 is the initial value.
Now to find the value of k, we need another equation given.
Let’s consider the doubling life of the quantity be 3 years, therefore:
 P0ek(3)=2P0.
Now on cancelling Po from both the sides we get:
e3k=2
On taking log to the base e on both the sides, we get:
lne3k=ln2
Now on simplifying we get:
3klne=ln2
Now we know that lne=1, therefore we get:
3k=ln2
Thus, k=ln23
Now on using a scientific calculator we get:
k=0.2310

Which is the value of k 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.