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

 Nov 22, 2018
 #1
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 \(f(x) = 2^x\). The y-coordinate never reaches 0, and the x and y-coordinates can be infinitely large. 

 

Hope this helps,

PM

 Nov 22, 2018
 #3
avatar+6097 
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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
edited by Rom  Nov 22, 2018
 #2
avatar+770 
0

Here is a graph: 

 

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

 

- PM

 Nov 22, 2018

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