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What else can I help you with?
exponential function?
Involves the function b^x where base ,b, is a positive number other than 1.
Does Exponential decay occurs if the base of an exponential function is a positive integer?
Yes.
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.
The base of an exponential function cannot be a negative number?
True
An exponential function is written as Fx equals a bx where the coefficient a is the base b is positive but not equal to 1 and the exponent x is any number?
a constant
An exponential function is written as Fx equals a bx where the coefficient a is a constant the base b is positive but not equal to 1 and the exponent x is?
any number
An exponential function is written as Fx equals a bx where the coefficient a is a constant the base b is but not equal to 1 and the exponent x is any number?
positive
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.
Why negative numbers don't have logarithim?
The logarithmic function is not defined for zero or negative numbers. Logarithms are the inverse of the exponential function for a positive base. Any exponent of a positive base must be positive. So the range of any exponential function is the positive real line. Consequently the domain of the the inverse function - the logarithm - is the positive real line. That is, logarithms are not defined for zero or negative numbers. (Wait until you get to complex analysis, though!)
In exponential growth functions the base of the exponent must be greater than 1. How would the function change if the base of the exponent were 1 How would the function change if the base of the expon?
"The base of the exponent" doesn't make sense; base and exponent are two different parts of an exponential function. To be an exponential function, the variable must be in the exponent. Assuming the base is positive:* If the base is greater than 1, the function increases. * If the base is 1, you have a constant function. * If the base is less than 1, the function decreases.
What is the logarithmic function and exponential function?
The exponential function is e to the power x, where "x" is the variable, and "e" is approximately 2.718. (Instead of "e", some other number, greater than 1, may also be used - this might still be considered "an" exponential function.) The logarithmic function is the inverse function (the inverse of the exponential function).The exponential function, is the power function. In its simplest form, m^x is 1 (NOT x) multiplied by m x times. That is m^x = m*m*m*...*m where there are x lots of m.m is the base and x is the exponent (or power or index). The laws of indices allow the definition to be extended to negative, rational, irrational and even complex values for both m and x.There is a special value of m, the Euler number, e, which is a transcendental number which is approx 2.71828... [e is to calculus what pi is to geometry]. Although all functions of the form y = m^x are exponential functions, "the" exponential function is y = e^x.Finally, if y = e^x then x = ln(y): so x is the natural logarithm of y to the base e. As with the exponential functions, the logarithmic function function can have any positive base, but e and 10 are the commonly used one. Log(x), without any qualifying feature, is used to represent log to the base 10 while logx where is a suffixed number, is log to the base b.
Can the base of an exponential function be a negatice number?
Yes, but perhaps only for exponents greater than 1 .
