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Basic exponential
Basic logarithmic
Applications
Other bases
100
This function is its own derivative
What is the exponential function?
100
It is the inverse of the natural exponential function.
What is the natural logarithm?
100
This is the amount of an investment after 5 years in an account whose balance is given by A(t) = 4000e0.08t.
What is $5,967.30?
100
The function log4x written in base e
What is ln(x) / ln(4)?
200
The derivative of f(x) = ex
What is ex
200
The derivative of f(x) = ln(x)
What is 1/x
200
This is the slope of the tangent line to the graph of f(x) = e-2x at x = 0.
What is -2?
200
The function f(x) = 2x written in base e
What is exln(2)?
300
The derivative of f(x) = e-4x
What is -4e-4x
300
The derivative of ln(4x3)
What is 3/x?
300
This function represents the instantaneous rate of change of f(x) = xln(x).
What is 1 + ln(x)?
300
It is the derivative of f(x) = 3x.
What is 3xln(3)?
400
The derivative of f(x) = 4x3e-x
What is -4x3 + 12x2e-x
400
The derivative of f(x) = (ln(x2))2
What is 4ln(x2)/x
400
The temperature T (deg. F) at which water boils for a given pressure p (psi) is given by T = 87.97 + 34.96ln(p) + 7.91p1/2. This quantity is the rate of change of temperature with respect to p pressure when the pressure is 60 psi.
What is 1.09 deg F/psi?
400
It is the derivative of f(x) = log(x).
What is 1/(xln(10))?
500
The derivative of f(x) = (ex + 1)/(x2 - ex)
What is (x2ex - 2xex)/(x2 - ex)2
500
The derivative of f(x) ln(xex/(x + 1))
What is 1/x + 1 - 1/(x + 1)
500
From 1985 through 2006 the number of cellphone towers y is modeled by y = 222827/(1 + 2677e-0.377t), where t = 5 corresponds to 1985. This date represents the approximate date when the rate of increase in the number of towers began to decrease.
What is 2001?
500
It is the derivative of f(x) = log4x2.
What is 2/(xln(4))?