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

Table of contents

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.

Parmis Kazemi
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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