Write an exponential growth function. Explain why your function represents exponential growth.
+775 \(f(x) = 2^x\). The y-coordinate never reaches 0, and the x and y-coordinates can be infinitely large.
Hope this helps,
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+6251 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)
\(\dfrac{2^{x_2}}{2^{x_1}} = 2^{x_2-x_1} = e^{\ln(2)(x_2-x_1)}\\ \ln(2) > 0\)
+775 Here is a graph:
https://www.desmos.com/calculator/0fkbsm68yi
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