Math Foundation
Everyday Australian words, slang and life-admin terms for migrants, students and workers — explained in plain English and 8 other languages.
Reviewed entries
35 entriesargument
nounIn maths, the input of a function, such as the number inside a logarithm.
In log₃(x + 2), the argument is x + 2 and it must be positive.
asymptote
nounA line that a graph approaches more and more closely but does not reach.
The graph of y = 2ˣ has a horizontal asymptote at y = 0.
base
nounIn maths, the number that is multiplied by itself in a power, or the number a logarithm is based on.
In 2⁵, the base is 2 and the exponent is 5.
The formula log_b(x) = log x ÷ log b, used to calculate logarithms in any base.
With the change of base formula, log₅ 20 = log 20 ÷ log 5.
common logarithm
nounA logarithm with base 10, written log x.
The common logarithm of 1,000 is 3.
Interest calculated on the original amount and on the interest already added.
With compound interest, $1,000 at 5% grows to about $1,276 after five years.
doubling time
nounThe time it takes for a growing quantity to double.
If a population has a doubling time of 10 years, it is four times larger after 20 years.
Euler's number
nounThe mathematical constant e, about 2.718, used in continuous growth and natural logarithms.
Continuous growth models use Euler’s number, e.
exponent
nounA small number written above another number to show how many times it is multiplied by itself.
In 5³, the exponent is 3.
Decrease by the same percentage over equal time periods.
The value of the car shows exponential decay of 15% a year.
An equation in which the variable is in an exponent.
To solve the exponential equation 3ˣ = 81, write 81 as 3⁴.
A function of the form f(x) = a·bˣ, where the variable is in the exponent.
Population growth can be modelled by an exponential function.
Increase by the same percentage over equal time periods.
The bacteria show exponential growth, doubling every hour.
growth factor
nounThe number b in an exponential model that each value is multiplied by, such as 1.05 for 5% growth.
A growth factor of 1.05 means a 5% increase each year.
half-life
nounThe time it takes for a quantity to fall to half its amount.
A substance with a half-life of 8 days has a quarter left after 16 days.
index
nounIn maths, the small number on a root sign showing which root to take, as in ³√8.
In ³√27, the index is 3, so we take the cube root.
inverse function
nounA function that reverses another function, written f⁻¹(x).
The inverse function of f(x) = 2x + 1 is f⁻¹(x) = (x − 1) ÷ 2.
logarithm
nounThe power to which a base must be raised to give a number: log_b(x) = y means bʸ = x.
log₂(8) = 3, because 2³ = 8.
An equation that contains a logarithm of the variable.
To solve the logarithmic equation log₂ x = 5, rewrite it as x = 2⁵.
A function of the form f(x) = log_b(x), the inverse of an exponential function.
The graph of a logarithmic function rises slowly and never touches the y-axis.
A scale where each step represents multiplying by the same factor, such as 10.
The Richter scale for earthquakes is a logarithmic scale.
A logarithm with base e, written ln x.
The natural logarithm of e² is 2.
An exponent less than zero, meaning the reciprocal: a⁻ⁿ = 1/aⁿ.
A negative exponent gives a fraction: 2⁻³ = 1/8.
nth root
nounA number that, raised to the power n, gives the original number.
The 4th root of 81 is 3, because 3⁴ = 81.
The size of a number in powers of ten.
The two distances differ by three orders of magnitude, a factor of about 1,000.