What is Exponential Growth?
Exponential growth can be simply defined as a pattern of data that shows greater increase over time and as a result curve of an exponential function is created. It is considered to be one of the most powerful tool of nature and commonly utilized in biological studies. The chances of growth increases manifold through this pattern and there are several examples. One of the most relatable example nowadays is the spread of Corona virus. It takes one patient or the carrier of corona virus to infect 2.5 individuals who are then going to infect 2.5 individuals each. To evaluate the scope of the infection, think about counting doubles – 1, 2, 4, 8, 16, 32, 64 and so on. How many times would you have to double to get to more than 1 million? 20. How many doubles to get to more than 16 million? 24.
There is an interesting story related to exponential growth that involves an English farmer who migrated to Australia and brought 24 rabbits with him. Thanks to exponential growth, in 6 years he was the proud owner of almost 6 million rabbits.
The concept of exponential growth is not only related to the field of biology. In physics, a free electron become accelerated by applying an external field and it frees up additional electrons. These electrons are also accelerated and create a cycle of growth indicating that physic also follow the rule of exponential growth. Nuclear chain reaction which the main concept of operation if unclear reactor is also an excellent example of exponential growth. Uranium cell undergoes fission and produce multiple neutrons as a result which are then absorbed by adjacent uranium atoms causing them to fission over and over again. Due to the exponential rate of increase, at any point in the chain reaction 99% of the energy will have been released in the last 4.6 generations. The example indicate the first 53 generations were latency period which lead to the actual explosion that normally takes 4 to 4 generations.
Importance of Exponential Growth
Accurate calculation of exponential growth is crucial to measure the pattern of reproduction. The estimation of growth and use of resources is commonly predicted utilizing the concept of exponential growth. The estimation of the reproduction cycle of endangered species is also calculated using the concept of exponential growth.
The exponential e is used while modeling the continuous growth of different species especially bacteria and radioactive decay. ‘e’ is the universal constant which indicates how fast the growth is and you can also include the time factor to assess that how much growth is increased in a certain time period.
The concept of the use of contraceptive to control the population was also possible due to calculation of exponential growth. Different researches indicated that we are utilizing natural resources such as water, land, and minerals at a drastic rate and soon there will be a shortage of resources if the population is not controlled. We are still lacking behind as the growth of human population is increasing at a drastic rate.
Exponential Growth Formula
There are two main function formula that are used to illustrate the concepts of growth and decay in applied situations. If a quantity grows by a fixed percent at regular intervals, the pattern can be depicted by these functions.
Remember that the original exponential formula was y = abx.
You will notice that in these new growth and decay functions,
the b value (growth factor) has been replaced either by (1 + r) or by (1 – r).
The growth “rate” (r) is determined as b = 1 + r.
The decay “rate” (r) is determined as b = 1 – r
a = initial value (the amount before measuring growth or decay)
r = growth or decay rate (most often represented as a percentage and expressed as a decimal)
x = number of time intervals that have passed
Let’s try to understand the formula through an example. The population of Hometown is 2016 was estimated to be 35,000 people with an annual rate of increase of 2.4%.
a) What is the growth factor for Hometown?
After one year the population would be 35,000 + 0.024(35000).
By factoring, we have 35000(1 + 0.024) or 35000(1.024).
The growth factor is 1.024. (Remember that growth factor is greater than 1.)
b) Write an equation to model future growth.
y = abx = a(1.014)x = 35000(1.024)x
c) Use the equation to estimate the population in 2020 to the nearest hundred people.
y = 35000(1.024)4 ≈ 38,482.91 ≈ 38,500
Why Exponential Calculator?
There are three points to consider whenever you want to calculate the growth rate or decay rate. The first one is preciseness – exponential growth calculator provide the precise results every time without any chance of error. The second important point is ease – exponential calculator is easy to use as it is specifically deign to be operated by adding the value and getting the result in a single click. The third major point is time – it takes minutes or hour to calculate exponential growth through manual procedure while exponential growth calculator can solve the same problem in mere seconds so it is time effective approach too!
Calculating growth and decay over a period of time is difficult and the chances of miscalculation and human error is higher. Considering the importance of results obtained from exponential growth formula, it becomes crucial that the results should be accurate. Rather than opting for the manually calculating the exponential growth, growth rate, or decay rate – it is better to use the calculators designed to cater to every aspect of exponential growth calculator. Our exponential calculator can help you solve your biology problems. If you want to calculate exponential growth rate of human, mice, or even bacteria – we have got you covered. Just put the values as specified, click calculate and get the accurate answer. The precise answer is just one click away – every time!