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If the question is, Is y = x4 an exponential function ? then the answer is no.An exponential function is one where the variable appears as an exponent.So, y = 4x is an exponential function.
262,144 = (2 x 10^5) + (6 x 10^4) + (2 x 10^3) + (1 x 10^2) + (4 x 10^1) + (4 x 10^0)
anything to the power of 0 is 1 except for 0. 0^0 is an indeterminate form. one way to demonstrate this is x^a/x^a = x^(a-a) which can be rewritten as 1=x^0. since e is not 0 e^0=1. this only works to numbers not infinity.
Exponential growth does not have an origin: it occurs in various situations in nature. For example if the rate of growth in something depends on how big it is, then you have exponential growth.
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