4.10.2: Key Equations
- Page ID
- 116112
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Key Equations
definition of the exponential function | |
definition of exponential growth | |
compound interest formula | |
continuous growth formula | is the number of unit time periods of growth is the starting amount (in the continuous compounding formula a is replaced with P, the principal) is the mathematical constant, |
General Form for the Translation of the Parent Function |
Definition of the logarithmic function | For if and only if |
Definition of the common logarithm | For if and only if |
Definition of the natural logarithm | For if and only if |
General Form for the Translation of the Parent Logarithmic Function |
The Product Rule for Logarithms | |
The Quotient Rule for Logarithms | |
The Power Rule for Logarithms | |
The Change-of-Base Formula |
One-to-one property for exponential functions | For any algebraic expressions and and any positive real number where if and only if |
Definition of a logarithm | For any algebraic expression S and positive real numbers and where if and only if |
One-to-one property for logarithmic functions | For any algebraic expressions S and T and any positive real number where if and only if |
Half-life formula | If the half-life is |
Carbon-14 dating | is the amount of carbon-14 when the plant or animal died is the amount of carbon-14 remaining today is the age of the fossil in years |
Doubling time formula | If the doubling time is |
Newton’s Law of Cooling | where is the ambient temperature, and is the continuous rate of cooling. |