2019-10-30T16:24:13+03:00[Europe/Moscow] en true exponential function, exponential growth, continuous, horizontal asymptote, half-life, compounded annually, equivalent equations, one-to-one function, logarithmic function, inverse function, product rule for logarithms, quotient rule for logarithms, power rule of logarithms, change-of-base formula, common logarithm, sound intensity, sound level, irrational constant, natural logarithm, Napierian logarithm, natural base exponential function, continuously compounded interest, Newton's law of cooling, exponential function, exponential growth, exponential decay, asymptote, growth factor, decay factor, exponential growth and decay, parent function (exp. fun), (exp. fun), (exp. fun), all transformations combined (exp. fun), continuously compound interest, logarithm, common logarithm, logarithmic scale, logarithmic function, parent functions (log. fun), (log. fun), (log. fun), all transformations together (log. fun), product property, quotient property, power property, change of base formula, exponential equation, natural logarithmic function, natural logarithmic function, the transformation from logs to exponentials. flashcards
Logarithm, Exponential and Logarithmic Functions

Logarithm, Exponential and Logarithmic Functions

  • exponential function
    Includes a constant raised to a variable power, f(x) = b^x. The base b must be positive but cannot equal 1
  • exponential growth
    the graph of an exponential function with a base greater than 1
  • continuous
    a smooth curve; there are no gaps in the curve for the domain
  • horizontal asymptote
    a horizontal line that the curve approaches but never reaches
  • half-life
    a fixed period of time in which something repeatedly decreases by half
  • compounded annually
    Interest that builds on itself at 12 month intervals
  • equivalent equations
    All values for x and y that make one equation true also make the other one true ( b^x = b^y if and only if x=y)
  • one-to-one function
    A function that matches each output with one input
  • logarithmic function
    the inverse of an exponential function
  • inverse function
    A function that reverses the effect of another function
  • product rule for logarithms
    states that the logarithm of a product of numbers equals the sum of the logarithms of the factors (log2 4*8 = ?)
  • quotient rule for logarithms
    states that the logarithm of the quotient of two numbers equals the difference of the logarithms of those numbers (log3 81/3 = ?)
  • power rule of logarithms
    states that the logarithm of a power of M can be calculated as the product of the exponent and the logarithm of M (log2 8^16 = ?)
  • change-of-base formula
    State log16 32 as an expression using 2 base logarithms
  • common logarithm
    logarithms with base 10
  • sound intensity
    a measure of how much power sound transmits
  • sound level
    measured in units called decibels (dB); provides a scale that relates how humans perceive sound to a physical measure of its power
  • irrational constant
    The number 'e'. A number that repeats without pattern
  • natural logarithm
    A logarithm with base 'e'
  • Napierian logarithm
    AKA natural logarithm, named after John Napier, a Scottish theologian and mathematician who discovered logarithms
  • natural base exponential function
    a function of form f(x) = ae^rx
  • continuously compounded interest
    interest that builds on itself at every moment f(t) = Pe^rt
  • Newton's law of cooling
    According to this law, the falling temperature obeys an exponential equation (y = ae^cx + T0, where T0 is the temperature surrounding the cooling object, x is the amount of time, and y is the current temperature)
  • exponential function
    a function that can be described by an equation of the form y= a*b^x, where b > 0 and b ≠ 1
  • exponential growth
    as the value of x increases, the value of y increaces
  • exponential decay
    as the value of x increases, the value of y decreases, approaching 0
  • asymptote
    A line that a graph approaches as x or y increases in absolute value
  • growth factor
    for exponential growth y= a*b^x, where b > 1, it is the value of b
  • decay factor
    for exponential decay, 0 < b <1, it is b
  • exponential growth and decay
    A(t) = a(1+r)^t A is the amount after t time periods a is the initial amount r is the rage of growth (r > 0) or decay (r<0) t is the number of time periods
  • parent function (exp. fun)
    y = b^x
  • (exp. fun)
    y = ab^x
  • (exp. fun)
    y = b^(x-h) + k
  • all transformations combined (exp. fun)
    y = ab^(x-h) + k
  • continuously compound interest
    A=Pe^rt A is the amount in account at time t P is the principal r is the interest rate (annual) t is time in years
  • logarithm
    this of a positive number y to the base b is defined as follows: If y=b^x, then log b y=x
  • common logarithm
    a logarithm to the base 10
  • logarithmic scale
    every one unit on the scale represents the unit multiplied by ten(1 unit=x10, 2 unit=10x10), when you use the logarithm of a quantity in stead of the quantity you are using the scale.
  • logarithmic function
    the function y=logx that is the inverse of the function y=10^x. the inverse of an exponential function.
  • parent functions (log. fun)
    y = log↓bx, b > 0, b ≠ 1
  • (log. fun)
    y = a log↓bx
  • (log. fun)
    y = log↓b(x-h) + k
  • all transformations together (log. fun)
    y = a log↓b(x - h) +k
  • product property
    log↓b mn = log↓b m+ log↓b n
  • quotient property
    log↓b m/n = log↓b m - log↓b n
  • power property
    log↓b m^n = n log↓b m
  • change of base formula
    logb M = logc M/ logc ^b, where M, b, and c are positive numbers, and b ≠ 1 and c ≠ 1.
  • exponential equation
    any equation that consists the form b^cx such as a = b^cx where the exponent includes a variable
  • natural logarithmic function
    y=In x or y = log↓ex, the inverse of the natural base exponential
  • natural logarithmic function
    if y = e^x then x = log↓ey = In y. the natural logarithmic function is the inverse of x = In y so you can write it as y = In x
  • the transformation from logs to exponentials.
    General relation log (base a) of x = y...............means a^y=x So what the calculator does is find that y number, or the power to which the base a has to be raised so that we get the number x;