Exponential functions look somewhat similar to functions you have seen before, in that they involve exponents, but there is a big difference, in that the variable is now the power, rather than the base. Previously, you have dealt with such functions as f(x) = x2, where the variable xwas the base and the number 2 was the power. In the case of exponentials, you will be dealing with functions such as g(x) = 2x, where the base is the fixed number, and the power is the variable.
Example:-
Q: A bank account balance, b, for an account starting with s dollars, earning an annual interest rate, r, and left untouched for nyears can be calculated as (an exponential growth formula). Find a bank account balance to the nearest dollar, if the account starts with $100, has an annual rate of 4%, and the money left in the account for 12 years.
A: b= s(1+r) x
b= 100(1+0.04)12
b= $160
Trigonometric functions, exponential functions are two common examples.
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Exponential relationship!
fundamental difference between a polynomial function and an exponential function?
"The" exponential function is ex. A more general exponential function is any function of the form AeBx, for any non-xero constants "A" and "B". Alternately, Any function of the form CDx (for constants "C" and "D") would also be considered an exponential function. You can change from one form to the other.
A __________ function takes the exponential function's output and returns the exponential function's input.
Trigonometric functions, exponential functions are two common examples.
Any function of the form aebx - for non-zero a and b - is exponential. For examples, just replace "a" and "b" with any non-zero number. Equivalently, any function of the form cdx - once again, for non-zero c and d - is exponential. Here, too, you can replace c and d with any number to get examples.
The parent function of the exponential function is ax
No. The inverse of an exponential function is a logarithmic function.
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Exponential relationship!
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.
If y is an exponential function of x then x is a logarithmic function of y - so to change from an exponential function to a logarithmic function, change the subject of the function from one variable to the other.
fundamental difference between a polynomial function and an exponential function?
No, an function only contains a certain amount of vertices; leaving a logarithmic function to NOT be the inverse of an exponential function.