Write an exponential growth function. Explain why your function represents exponential growth.

Guest Nov 22, 2018

#1**+1 **

\(f(x) = 2^x\). The y-coordinate never reaches 0, and the x and y-coordinates can be infinitely large.

Hope this helps,

PM

PartialMathematician
Nov 22, 2018

#3**+1 **

according to this description

\(y = x^2 + 1\)

represents exponential growth

exponential growth occurs when the ratio of two values at different times is exponential in the difference between those times with a positive constant.

i..e

\(\dfrac{f(t_1)}{f(t_0)} \sim e^{\lambda(t_1-t_0)},~\lambda > 0\)

In your example (which is indeed exponential growth)

\(\dfrac{2^{x_2}}{2^{x_1}} = 2^{x_2-x_1} = e^{\ln(2)(x_2-x_1)}\\ \ln(2) > 0\)

Rom
Nov 22, 2018

#2**+2 **

Here is a graph:

https://www.desmos.com/calculator/0fkbsm68yi

- PM

PartialMathematician
Nov 22, 2018