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.