Exponential Functions

Rate of Change

A normal resting heart rate for adults ranges from 60 to 100 beats a minute. Generally, a lower heart rate at rest implies more efficient heart function and better cardiovascular fitness. For example, a well-trained athlete might have a normal resting heart rate closer to 40 beats a minute.

Exponential Decay

Exponential decay is the decrease in a quantity according to the law. (1) for a parameter and constant (known as the decay constant), where is the exponential function and is the initial value.

Common Ratio

For a geometric sequence or geometric series, the common ratio is the ratio of a term to the previous term. This ratio is usually indicated by the variable r. Example: The geometric series 3, 6, 12, 24, 48, . . . has common ratio r = 2.

Function Notation

Function notation is the way a function is written. It is meant to be a precise way of giving information about the function without a rather lengthy written explanation. The most popular function notation is f (x) which is read "f of x".

Geometric Sequence

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3.

Explicit Form

It defines the sequence as a formula in terms of n. It may be written in either subscript notation a n, or in functional notation, f (n). Sequence: {10, 15, 20, 25, 30, 35, ...}. Find an explicit formula. This example is an arithmetic sequence(the same number, 5, is added to each term to get to the next term).

Exponential Form

Rules for writing in exponential form: An exponent is used to tell how many times a number, called the base is used as a factor: Step 1 - Multiply the base number times the base number as many times as the value of the exponent. Example: 56 = 5 • 5 • 5 • 5 • 5 • 5 = 15625.

Relative Maximum

The highest point in a particular section of a graph. Note: The first derivative test and the second derivative test are common methods used to find maximum values of a function. See also. Global maximum, absolute maximum, global minimum, absolute minimum, local minimum, relative minimum, extremum.

Relative Minimum

The lowest point in a particular section of a graph. Note: The first derivative test and the second derivative test are common methods used to find minimum values of a function. See also. Global minimum, absolute minimum, global maximum, absolute maximum, local maximum, relative maximum, extremum.

Exponential Equation

When both sides of the equation have the same base, the exponents on either side are equal by the property if , then . Important logarithmic rules used to solve exponential equations include: Exponential equations are also solved using logs, either common (log) or natural (ln).

Exponential Function

a function whose value is a constant raised to the power of the argument, especially the function where the constant is e.

Exponent

a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression (e.g., 3 in 23 = 2 × 2 × 2).

Domain

a specified sphere of activity or knowledge.

Now-Next

couldn't find???

Exponential Growth

growth whose rate becomes ever more rapid in proportion to the growing total number or size.

Intercepts

obstruct (someone or something) so as to prevent them from continuing to a destination.

Constant

occurring continuously over a period of time.

Base

situate as the center of operations.

Range

the area of variation between upper and lower limits on a particular scale.