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For an exponential function: General equation of exponential decay is A(t)=A0e^-at The definition of a half-life is A(t)/A0=0.5, therefore: 0.5 = e^-at ln(0.5)=-at t= -ln(0.5)/a For exponential growth: A(t)=A0e^at Find out an expression to relate A(t) and A0 and you solve as above
An algorithm that completes in "polynomial time" is faster to solve than an algorithm that completes in "exponential time" in most of the important cases where it needs to be solved. An algorithm that completes in "polynomial time" the time to solve is always determinable by a polynomial equation (e.g. x^2, x^4+7*x^3+12*x^2+x+19, x^8392). An algorithm that completes in "exponential time" the time to solve can only be determined an exponential equation (e.g. 2^x, e^x, 10^x, 982301^x). Exponential equations give larger value answers than polynomial equations after a certain input value and then increase progressively faster. This makes "exponential time" algorithms take much longer than "polynomial time" algorithms to solve, often making many of them effectively unsolvable for certain cases. Many of the most important algorithms needed to solve real world problems are "exponential time" algorithms.
The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)
logb x = a According to the definition of the logarithm, a is the number that you have to exponentiate b with to get x as a result. Therefore: ba = x
Basically, in an exponential expression (or equation) you have the independent variable in the exponent. For example: 5 times 10x The general form of an exponential function can be written as: abx or: aekx where a, b, and k are constants, and e is approximately 2.718. Note that just having a power doesn't mean you have an exponential equation. For example, in x3 the variable does NOT appear in the exponent, so it is not an exponential expression.