##### Asked by: Soulimane Nesme

asked in category: General Last Updated: 4th June, 2020# How do you solve for K in exponential growth?

**Now some algebra to solve for k:**

- Divide both sides by 3:6 = e
^{2k} - Take the natural logarithm of both sides:ln(6) = ln(e
^{2k}) - ln(e
^{x})=x, so:ln(6) = 2k. - Swap sides:2k = ln(6)
- Divide by 2:
**k**= ln(6)/2.

Also question is, how do you model exponential growth?

Systems that exhibit **exponential growth** follow a **model** of the form y=y0ekt. In **exponential growth**, the rate of **growth** is proportional to the quantity present. In other words, y′=ky. Systems that exhibit **exponential growth** have a constant doubling time, which is given by (ln2)/k.

Also, what is exponential form? "**Exponential form**" simply means a numeric **form** involving exponents. One way to write such a number is by recognizing that each position represents a power (exponent) of 10. There is also an **exponential form** called "scientific notation" which is used extensively in science.

Regarding this, how do we calculate growth rate?

To calculate **growth rate**, start by subtracting the past value from the current value. Then, divide that number by the past value. Finally, multiply your answer by 100 to express it as a percentage. For example, if the value of your company was $100 and now it's $200, first you'd subtract 100 from 200 and **get** 100.

What is the formula for exponential decay?

In mathematics, **exponential decay** describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the **formula** y=a(1-b)^{x} wherein y is the final amount, a is the original amount, b is the **decay** factor, and x is the amount of time that has passed.