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

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

Guest Nov 22, 2018
#1
+656
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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

PartialMathematician  Nov 22, 2018
#3
+3190
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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
+656
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Here is a graph:

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

- PM

PartialMathematician  Nov 22, 2018