Jak używać funkcji TANH w Excelu
Introduction to the TANH Function
The TANH
function, known as the hyperbolic tangent, is a mathematical function available in both Microsoft Excel and Google Sheets. It is especially useful in various fields such as engineering, mathematics, finance, and data analysis. It returns the hyperbolic tangent of a given number.
Syntax and Examples
The syntax for the TANH
function is straightforward:
=TANH(number)
Here, number refers to the value for which the hyperbolic tangent is calculated.
Examples of usage in a spreadsheet include:
=TANH(0)
– Returns 0, as the hyperbolic tangent of zero is zero.=TANH(1)
– Returns approximately 0.7616, which is the hyperbolic tangent of one.
Applications of the Function in Practical Scenarios
Population Growth Analysis
Consider a study on the population growth of a certain animal species, which you wish to model using a hyperbolic function. Assume that population growth over time (t) can be described by:
Population(t) = maximum_population * TANH(0.03 * t)
For instance, if the maximum forecasted population is 1000 individuals, using Excel or Google Sheets, you can compute the population after 10, 20, and 30 days:
Time (t) | Formula | Result |
---|---|---|
10 days | =1000 * TANH(0.03 * 10) |
258.18 |
20 days | =1000 * TANH(0.03 * 20) |
462.11 |
30 days | =1000 * TANH(0.03 * 30) |
576.68 |
Application in Finance to Assess Investment Risk
Suppose you are a financial analyst looking to evaluate investment risk that changes over time and you want to use the TANH function to smooth the risk values, which tend to an asymptotic level. This scenario can be modeled as follows:
Risk(t) = max_risk * TANH(scaling * t)
For simplicity, let”s assume max_risk
as 100%, and scaling
as 0.05. We can then explore how the risk changes over time (t=0 to t=50) in steps of 10:
Time (t) | Formula | Result |
---|---|---|
0 days | =100 * TANH(0.05 * 0) |
0% |
10 days | =100 * TANH(0.05 * 10) |
48.49% |
20 days | =100 * TANH(0.05 * 20) |
76.10% |
30 days | =100 * TANH(0.05 * 30) |
87.97% |
40 days | =100 * TANH(0.05 * 40) |
93.59% |
50 days | =100 * TANH(0.05 * 50) |
96.42% |
In this scenario, the hyperbolic function helps understand how the risk evolves over time, approaching asymptotically to the maximum risk value.
Więcej informacji: https://support.microsoft.com/pl-pl/office/tanh-funkcja-017222f0-a0c3-4f69-9787-b3202295dc6c