Enhance Your Learning with Exponential Functions and Logarithms Flash Cards for quick learning
A function of the form f(x) = a^x, where a is a positive constant and x is a real number.
A type of growth where the quantity increases at a constant percentage rate over equal intervals of time.
A type of decay where the quantity decreases at a constant percentage rate over equal intervals of time.
An equation in which the variable appears in the exponent.
The inverse operation of exponentiation. If y = a^x, then x = log_a(y), where a is the base.
A logarithm with base 10, denoted as log(x) or log10(x).
A logarithm with base e, where e is the mathematical constant approximately equal to 2.71828. It is denoted as ln(x).
An equation in which the variable appears inside a logarithm.
Properties such as the product rule, quotient rule, and power rule that apply to exponential functions.
Properties such as the product rule, quotient rule, and power rule that apply to logarithmic functions.
A graph that shows the relationship between an exponential function and its input values.
A graph that shows the relationship between a logarithmic function and its input values.
The formula A = P(1 + r/n)^(nt) used to calculate the future value of an investment with compound interest.
The formula A = P(1 - r/n)^(nt) used to calculate the future value of a decaying quantity.
The inverse of a logarithmic function is an exponential function, and vice versa.
Equations in the form a^x = a^y, where a is a positive constant.
Equations in the form a^x = b^y, where a and b are positive constants and a ≠ b.
Equations in the form log_a(x) = log_a(y), where a is a positive constant.
Equations in the form log_a(x) = log_b(y), where a and b are positive constants and a ≠ b.
Mathematical models that describe the growth or decay of a quantity over time.
The time it takes for half of a radioactive substance to decay.
Interest that is compounded continuously, using the formula A = P*e^(rt), where e is the mathematical constant.
Properties such as the product rule, quotient rule, and power rule that apply to logarithms.
A formula used to convert logarithms from one base to another.
Applications of exponential functions in various fields such as finance, population growth, and radioactive decay.
Applications of logarithms in various fields such as pH scale, sound intensity, and earthquake magnitude.
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