数学基础
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已审核词条
35 个词条argument
noun真数
In 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.
在log₃(x + 2)中，真数是x + 2，必须为正。asymptote
noun渐近线
A 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.
y = 2ˣ的图像在y = 0处有水平渐近线。base
noun底数
In 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.
在2⁵中，底数是2，指数是5。换底公式
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.
用换底公式，log₅ 20 = log 20 ÷ log 5。common logarithm
noun常用对数
A logarithm with base 10, written log x.
The common logarithm of 1,000 is 3.
1,000的常用对数是3。复利
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.
按复利计算，1,000美元以5%的利率存五年约增至1,276美元。doubling time
noun倍增时间
The 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.
倍增时间为10年的人口，20年后变为四倍。Euler's number
noun自然常数e
The mathematical constant e, about 2.718, used in continuous growth and natural logarithms.
Continuous growth models use Euler’s number, e.
连续增长模型使用自然常数e。
exponent
noun指数
A small number written above another number to show how many times it is multiplied by itself.
In 5³, the exponent is 3.
在5³中，指数是3。指数衰减
Decrease by the same percentage over equal time periods.
The value of the car shows exponential decay of 15% a year.
这辆车的价值每年按15%指数衰减。指数方程
An equation in which the variable is in an exponent.
To solve the exponential equation 3ˣ = 81, write 81 as 3⁴.
解指数方程3ˣ = 81时，把81写成3⁴。指数函数
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.
人口增长可以用指数函数建模。指数增长
Increase by the same percentage over equal time periods.
The bacteria show exponential growth, doubling every hour.
细菌呈指数增长，每小时翻一番。growth factor
noun增长因子
The 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.
增长因子1.05表示每年增长5%。half-life
noun半衰期
The 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.
半衰期为8天的物质，16天后剩下四分之一。index
noun根指数
In 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.
在³√27中，根指数是3，所以求立方根。inverse function
noun反函数
A function that reverses another function, written f⁻¹(x).
The inverse function of f(x) = 2x + 1 is f⁻¹(x) = (x − 1) ÷ 2.
f(x) = 2x + 1的反函数是f⁻¹(x) = (x − 1) ÷ 2。logarithm
noun对数
The 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.
因为2³ = 8，所以log₂(8) = 3。对数方程
An equation that contains a logarithm of the variable.
To solve the logarithmic equation log₂ x = 5, rewrite it as x = 2⁵.
解对数方程log₂ x = 5时，把它改写成x = 2⁵。对数函数
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.
对数函数的图像缓慢上升，永远不会碰到y轴。对数刻度
A scale where each step represents multiplying by the same factor, such as 10.
The Richter scale for earthquakes is a logarithmic scale.
地震的里氏震级是对数刻度。自然对数
A logarithm with base e, written ln x.
The natural logarithm of e² is 2.
e²的自然对数是2。负指数
An exponent less than zero, meaning the reciprocal: a⁻ⁿ = 1/aⁿ.
A negative exponent gives a fraction: 2⁻³ = 1/8.
负指数会得到分数：2⁻³ = 1/8。nth root
nounn次方根
A number that, raised to the power n, gives the original number.
The 4th root of 81 is 3, because 3⁴ = 81.
因为3⁴ = 81，所以81的四次方根是3。数量级
The size of a number in powers of ten.
The two distances differ by three orders of magnitude, a factor of about 1,000.
两段距离相差三个数量级，约1,000倍。