8.8K
ITExponential Functions graphs! #iteachalgebra #math #algebra #mathematics #iteachmath #teacher #mathteacher
@iteachalgebra
#Exponential Function In Statistics
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OMGraphing exponential functions by @iteachalgebra
Excellent explanation, we hope you can take advantage of it!🤩
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@omegalearningdoral
708.2K
MAIn mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. The exponential of a variable x is denoted exp(x) or eˣ, with the two notations used interchangeably. It is called exponential because its argument can be seen as an exponent to which a constant number e ≈ 2.718, the base, is raised. There are several other definitions of the exponential function, which are all equivalent although being of very different nature.
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the 18th century.
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@mathvibes01
2.3K
HOEven though e^x is undefeatable in its own variable (x), it becomes powerless when viewed through a different lens (y). A fun way to illustrate the power of variable context in differentiation.
y (a different variable) yields 0, because e^x is a constant with respect to y.
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@how_it_works203
11.3K
THFunction Graph & Withdrawal - Secondary Second #Second_Year_Scientific_Stream📚 #Mathematics_Step_by_Step #Graphing_of_a_Function #Numerical_Functions
@theti84calc
814.3K
MAThe constants e and pi are two of the most important numbers in mathematics, each appearing in countless areas of study. Pi, which is approximately 3.14159, is defined as the ratio of a circle’s circumference to its diameter. It is most often connected to geometry and trigonometry, but it also shows up in unexpected places such as probability, statistics, and even in formulas describing waves and heat transfer. Pi is an irrational number, meaning its decimal expansion goes on forever without repeating, and it is also transcendental, meaning it cannot be expressed as the solution to any simple polynomial equation.
The number e, approximately 2.71828, is known as the base of natural logarithms and arises most naturally in problems involving growth and change. It can be defined through the process of compounding, as in the limit of (1 + 1/n) raised to the power of n as n grows larger and larger. This makes e essential in modeling things like population growth, financial interest, and exponential decay. Like pi, e is irrational and transcendental, and its role in calculus is fundamental, especially because the exponential function with base e is the only function whose rate of change is equal to its value. When combined with pi, it leads to one of the most elegant equations in mathematics: Euler’s identity, which ties together e, pi, and the imaginary unit in a remarkably simple way.
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@mathswithmuza
3.0K
MAGraphs of the functions #graphs #viralreels #viral #maths
@mathematicshub01
2.6K
HAIntegration of Exponential Functions – Quick Quiz: Solve in 1 Minute! You Don’t Know These Tricks! #math #integration #exponential #quiz #quiz #sat
@happymath.academy
16.8K
THThe exponential curve is a mathematical function of the form y = e^x, where e is Euler’s number, approximately equal to 2.718. This curve grows rapidly and is fundamental in modeling processes like population growth, compound interest, and natural phenomena.
#math #learning #animation #exponential #reels
@themathcentral
3.1K
TUConfused by 7^x = 70? Let’s break it down!
This is called an exponential equation — the unknown value (x) is in the power.
But how do we “get the x down”?
That’s where logarithms come in! Logs are the opposite of exponents — like how subtraction is the opposite of addition.
⸻
Here’s how we solve it:
1️⃣ Start with:
7^x = 70
2️⃣ Take log of both sides (logarithms help us deal with exponents):
log(7^x) = log(70)
3️⃣ Now use the log rule:
log(a^b) = b · log(a)
This rule lets us bring the x to the front:
x · log(7) = log(70)
4️⃣ Solve for x:
x = log(70) / log(7)
x ≈ 1.8451 / 0.8451 ≈ 2.18
So… x ≈ 2.18!
⸻
Tutorly.sg helps students truly understand the “why” behind the steps.
Don’t just memorise — learn with confidence!
Start for FREE today at Tutorly.sg
✏️📚🧠
@tutorly.sg
154.6K
TH📈 Extrema of a Function: Peaks & Valleys! ⛰️✨
• Extrema are the highest and lowest points of a function—its maximums and minimums. They’re where curves reach their peaks or dips! 🎯
• Why it’s awesome:
Finding extrema helps us optimize—whether it’s max profit, min cost, or best design. ⚡
• Where it’s used:
💸 Economics – Maximizing revenue & minimizing risk
🌍 Engineering – Strongest structures with least material
🔬 Physics – Energy minimization in natural systems
🧠 Math – Optimization & calculus fundamentals
#mathematics #physics #animation #derivatives #calculus #geometry #functions #algebra #fyp #likeme #views
@the_mathsensei
1.1M
ALLogarithms turn outputs back into inputs - they’re the inverse of exponentials. In this short explainer, we reflect y = 2^x in y = x, derive x = log₂(y), solve 2^x = 10, and show the change-of-base trick for your calculator. Perfect quick revision for A-Level Maths.
#ALevelMaths #MathsEducation #Logarithms #ExponentialFunctions #SixthForm #MathsRevision #STEMEducation #EdexcelMaths #GCSEMaths #FurtherMaths
@alevel.maths
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