Mathematical Calculators

# Exponential Growth Calculator

The exponential Growth Calculator calculates the final price of a quantity based on its initial values, rate of growth, and time.

#### Exponential Growth Calculator

x(t) = x₀ • (1 + r / 100) t
%

 ◦How to calculate exponential Growth
You can use the exponential growth calculator for many different processes. The exponential Growth Formula should be used as a guideline.
ₓ₍ₜ₎ ₌ ₓ₀ * ₍₁ ₊ ᵣ/₁₀₀₎ₜ
You should note that the exponential rate of growth, r can be any number. However, this calculator can also be used as a decay calculator. r represents the rate at which the material decays, which should range between 0 and 100%. You cannot have a decline greater than 100% of the initial amount, because it would lead to a negative number.
The exponential growth equation can be used in radiocarbon dat, and PCR (you will find the reason with our annealing temp calculator), along with calculating compound interest.

## How to calculate exponential Growth

Take the following example: The population of a small town at the start of 2019 was 10,000. The population of the city has been growing at a steady 5% annual rate. What can you do to determine the projected population by 2030? We can see that the x0 initial population value equals 10,000. The growth rate is 5%.
We should therefore use the exponential growth formula:
ₓ₍ₜ₎ ₌ ₁₀,₀₀₀ * ₍₁ ₊ ₀.₀₅₎ₜ ₌ ₁₀,₀₀₀ * ₁.₀₅ₜ
Here t is how many years have passed since 2019. We should use t=11 in our example to represent the year 2030. This is the difference in the number of years between 2030 (and the initial year 2019). Finally, here's what we get:
ₓ₍₁₁₎ ₌ ₁₀,₀₀₀ * ₁.₀₅₁₁ ₌ ₁₇,₁₀₃
Accordingly, the estimated population of our small town in 2030 will be around 17,103.  Article author
Parmis Kazemi
Parmis is a content creator who has a passion for writing and creating new things. She is also highly interested in tech and enjoys learning new things.

###### Exponential Growth Calculator English
Published: Tue May 31 2022
In category Mathematical calculators
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