Exponential Function: Exponential functions are one-to-one functions. graph passes the horizontal line test - its inverse is also a function.Exponential Growth Function: when a > 0 and the b is greater than 1, the graph will be increasing (growing).
Exponential Decay Function:when a > 0 and the b is between 0 and 1, the graph will be decreasing (decaying).
Natural base:The function f(x) = ex is called the exponential function, and its inverse is the natural logarithm, or logarithm to base e.
Common Logarithm: A logarithm to the base of 10.
Exponential Equations: An exponential equation is one in which a variable occurs in the exponent.
Logarithmic Equations: A logarithmic equation is an equation that involves the logarithm of an expression containing a variable.
Parent Function or Exponential Growth Function: A parent function is the simplest function of a family of functions. The "Parent" Graph: The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II.
Compound Interest: When the interest rate is applied to the original principal and any accumulated interest, this is called compound interest.
Natural Base Function: Alternatively, if the exponential function has been defined first, say by using an infinite series, the natural logarithm may be defined as its inverse function, i.e., ln is that function such that exp(ln(x)) = x.
Continuously Compounded Interest: Continuously Compounded Interest is a great thing when you are earning it!Continuously compounded interest means that your principal is constantly earning interest and the interest keeps earning on the interest earned!
Properties of Logarithms: The logarithm base b of a number xis the power to which b must be raised in order to equal x. This is written logb x. For instance, because . Logshave four basic properties: Product Rule: The log of a product is equal to the sum of the log of the first base and the log of the second base ( ).
Change of Base Formula: A formula that allows you to rewrite a logarithm in terms of logs written with another base. This is especially helpful when using a calculator to evaluate a log to any base other than 10 or e. Assume that x, a, and b are all positive.
Exponential Decay Function:when a > 0 and the b is between 0 and 1, the graph will be decreasing (decaying).
Natural base:The function f(x) = ex is called the exponential function, and its inverse is the natural logarithm, or logarithm to base e.
Common Logarithm: A logarithm to the base of 10.
Exponential Equations: An exponential equation is one in which a variable occurs in the exponent.
Logarithmic Equations: A logarithmic equation is an equation that involves the logarithm of an expression containing a variable.
Parent Function or Exponential Growth Function: A parent function is the simplest function of a family of functions. The "Parent" Graph: The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II.
Compound Interest: When the interest rate is applied to the original principal and any accumulated interest, this is called compound interest.
Natural Base Function: Alternatively, if the exponential function has been defined first, say by using an infinite series, the natural logarithm may be defined as its inverse function, i.e., ln is that function such that exp(ln(x)) = x.
Continuously Compounded Interest: Continuously Compounded Interest is a great thing when you are earning it!Continuously compounded interest means that your principal is constantly earning interest and the interest keeps earning on the interest earned!
Properties of Logarithms: The logarithm base b of a number xis the power to which b must be raised in order to equal x. This is written logb x. For instance, because . Logshave four basic properties: Product Rule: The log of a product is equal to the sum of the log of the first base and the log of the second base ( ).
Change of Base Formula: A formula that allows you to rewrite a logarithm in terms of logs written with another base. This is especially helpful when using a calculator to evaluate a log to any base other than 10 or e. Assume that x, a, and b are all positive.