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An exponential growth function represents a quantity that has a constant halving time?
That would be an exponential decay curve or negative growth curve.
When is an exponential expression completely simplified?
when there is no negative exponentswhen there is a minimal number of bases~
A logarithmic function takes the exponential function's and returns the exponential function's input?
output
Is an exponential function is the inverse of a logarithmic function?
No, an function only contains a certain amount of vertices; leaving a logarithmic function to NOT be the inverse of an exponential function.
What is the domain of logarithm and exponential function?
Domain of the logarithm function is the positive real numbers. Domain of exponential function is the real numbers.
The base of an exponential function cannot be a negative number?
True
Can a exponential functions be a negative number?
Exponential functions of the form ( f(x) = a \cdot b^x ), where ( a ) is a constant and ( b ) is a positive base, cannot yield negative values if ( a ) is positive. However, if ( a ) is negative, the function can take on negative values for certain inputs. In general, exponential functions are always positive when ( a ) is positive and ( b ) is greater than zero, but they can be negative if ( a ) is negative.
Can an exponential decay model have negative y values?
An exponential function can have negative y-values. However, a real-world exponential decay model will never have negative values. Think of it this way... If you divide a positive number by 2 (or take half of it) and then divide that next number by 2, you will never reach or go below 0. For Example: 20, 10, 5, 2.5, 1.25, 0.625, 0.3125, etc. (Each number is half of the number before it.)
What happened if the base of exponential function is less than zero?
If the base of an exponential function is less than zero, the function can exhibit complex behavior. Specifically, if the base is a negative number, the function will not be defined for all real numbers, as it will yield complex numbers for non-integer exponents. Consequently, the exponential function may oscillate between positive and negative values, depending on the exponent's parity, which complicates its interpretation in real-world applications. Thus, exponential functions are typically defined with a positive base for meaningful real-valued outputs.
A function takes the exponential function's output and returns the exponential function's input?
A __________ function takes the exponential function's output and returns the exponential function's input.
An exponential growth function represents a quantity that has a constant halving time?
That would be an exponential decay curve or negative growth curve.
What is the parent function for the exponential function?
The parent function of the exponential function is ax
Why radioactivity is exponential?
The number of atoms that decay in a certain time is proportional to the amount of substance left. This naturally leads to the exponential function. The mathematical explanation - one that requires some basic calculus - is that the only function that is its own derivative (or proportional to its derivative) is the exponential function (or a slight variation of the exponential function).
Is the inverse of an exponential function the quadratic function?
No. The inverse of an exponential function is a logarithmic function.
Do exponential functions have a domain that includes all real numbers?
Yes, exponential functions have a domain that includes all real numbers. This means that you can input any real number into an exponential function, such as ( f(x) = a^x ), where ( a ) is a positive constant. The output will always be a positive real number, regardless of whether the input is negative, zero, or positive.
How do you write the standard number -75.116 in exponential notation?
Negative numbers cannot be written in exponential notation. The rules require the number to be between 1.0-9.9.
When is an exponential expression completely simplified?
when there is no negative exponentswhen there is a minimal number of bases~
