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Q: An exponential decay function represents a quantity that has a constant doubling time?

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False

That would be an exponential decay curve or negative growth curve.

An exponential function is of the form y = a^x, where a is a constant. The inverse of this is x = a^y --> y = ln(x)/ln(a), where ln() means the natural log.

This question appears to relate to some problem for which we have no information. The graph of an exponential function shows a doubling at regular intervals. But we are not told what the role is of b, so we cannot comment further.

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False

True

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That would be an exponential decay curve or negative growth curve.

The only non-exponential function that has this property would be a function that has the constant value of zero.

y = ax, where a is some constant, is an exponential function in x y = xa, where a is some constant, is a power function in x If a > 1 then the exponential will be greater than the power for x > a

an exponential function flipped over the line y=x

An exponential function of the form a^x eventually becomes greater than the similar power function x^a where a is some constant greater than 1.

Exponential Decay - Apex

The graph of a linear function is a line with a constant slope. The graph of an exponential function is a curve with a non-constant slope. The slope of a given curve at a specified point is the derivative evaluated at that point.

An exponential function is of the form y = a^x, where a is a constant. The inverse of this is x = a^y --> y = ln(x)/ln(a), where ln() means the natural log.

An exponential function is any function of the form AeBx, where A and B can be any constant, and "e" is approximately 2.718. Such a function can also be written in the form ACx, where "C" is some other constant, used as the base instead of the number "e".

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