All Questions
Tagged with mathematical-modeling exponential-function
43 questions
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28
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Smooth periodic extension of a function on $[0,1)^d$ to $\mathbb R^d$
Here is my goal: Given $n\in\mathbb N_0\uplus\{\infty\}$, I want to construct a function $q:[0,1)^d\to(0,\infty)$ such that $q\circ\iota\in C^n(\mathbb R^d)$, where $$\iota:\mathbb R^d\to[0,1)^d\;,\;\;...
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1
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78
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Isolating $z$ in the equation $x - 1 = - \frac{1-y^{z+1}-0.5(1-y^z)}{(1-y)y^z}$ [closed]
I have a formula with multiple unknowns:
$$x - 1 = - \frac{1-y^{z+1}-0.5(1-y^z)}{(1-y)y^z}$$
The way it is setup now allows to easily calculate $x$, but I would like to reformulate it to isolate $z$, ...
- 25
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1
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Modelling exponential growth with individual limited lifetime/death
The Wikipedia article on Diatoms states that:
an assemblage of living diatoms doubles approximately every 24 hours by asexual multiple fission; the maximum life span of individual cells is about six ...
- 109
1
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1
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65
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Population of randomly dividing cell
I was really curious. What if, instead of dividing into two every day, the cell divides into one, two, or three, and the probability of all three cases is $1/3$. Initially, there's one. After n days, ...
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2
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139
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What is meant by "increases exponentially with time"?
The following qeustion states "you may assume Phoebe's speed increases exponentially with time", but only provides 2 data points from which to derive the model. Is this question lacking ...
- 103
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421
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Lion and wildebeest population modelling question issue
I am a student completing A levels and recently received the following question in an official mock exam for the Edexcel A-level in Mathematics. Having discussed the question extensively with my peers ...
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1
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75
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How do i write the exponential decay for this? [closed]
At this time, the number of people who use a particular health plan is 19,250. The number of people who use the plan is expected to decrease by 14% each year.
Write an equation of the type you just ...
- 3
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26
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Find one sided limit to show equivalence
I'm working on a problem that looks at growth models and I'm trying to show that the equation,
$\frac{dN}{dt}$ = $aN^{\gamma}$ - $bN^{\gamma}$($\frac{N^{\gamma -1} - 1}{1 - \gamma}$)
is equivalent to ...
- 77
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1
answer
3k
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relationship between doubling time and growth rate
I have been trying to plot the growth rate in new daily COVID-19 cases (not cumulative) over time for a country. I have smoothed out the daily cases using a 7-day moving average. I then take the ...
- 1,071
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41
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Exponential growth in contagious disease models
I am a student at the early stage of learning differential equations. In my textbook there is an introduction of the SIR model, and later I also found this Covid prediction model published in 2020.
...
- 21
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42
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Investment modeling
Exponential growth of a capital is given by the expression
$$C(t)=C_0(1+r)^t$$
A typical shape of investments is initially decreasing and gradually becoming exponential later on. This behavior can be ...
- 5,337
2
votes
1
answer
68
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When do I decide a logistic model with no roots equals 0?
I have a logistic model function:
$$ y=\frac{424.92}{1+0.37027e^{0.000715x}}$$
This exponential model has an asymptote at $y=0$, and hence doesn't ever meet the $x$-axis. However, I need to discern ...
- 33
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27
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Combining multiple exponential growths and decays in a model
Say I have a capacitor to which I apply a square pulse of power for $t_1$. Potential will grow to unity (fully charged) exponentially over time, and decay back to 0 (no charge) exponentially over time....
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5
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1
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350
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Fibonacci and the spreading of viruses
I tried to understand better the spreading of a virus on a case-by-case basis, not by differential or difference equations as in SIR and SEIR models with possibly non-integer rates and time constants.
...
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one function for 3 scenarios
Just wondering, is there a function that depends and a small number of parameters and can model these 3 scenarios (depending on the chosen parameters):
The first is a constant, the second a log-...
- 129
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2
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658
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How to model a quasi-exponential function?
This is the graphic of official daily deaths caused by Covid-19 in Brazil.
And this is the same graphic with an exponential model in red. We see the model don't fit the data.
The misadjustment is ...
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1
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127
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Epidemiology and the corona virus [closed]
How would we model the current spread and death rate of the novel corona virus in the UK: Covid19 death, case graph?
Is there a way we could do this or are there too many unknown variables that we don’...
1
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1
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260
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Mathematical model of spread of disease - exponential growth, herd immunity, and normal distribution [closed]
Covid-19 made me speculate of how to mathematically model the spread of a disease.
So let's say there's some virus that has a basis reproduction number R0 = 3 (so one infected person does infect ...
- 599
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1
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81
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$e^{pt}$ or $(1+p)^t$ What is the difference in modeling exponential growth and decay?
I would like to better understand, when the function $e^{pt}$ is the "better" choice and when (if at all) $(1+p)^t$ should be used.
To give a classic example: Say we want to model radioactive decay ...
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2
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188
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How does population growth relate to $e$?
Say that there is a population of $10,000$. From year $0$ to year $1$, we know that the population has grown to $20,000$. How might I model this growth?
It clearly isn't sensible to say that the ...
- 21.8k
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1
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239
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Solution for differential equation describing linear input and exponential decay
I try to model the concentration over time when there's an linear input and an exponential output (i.e. exponential decay) with known half-life.
Input(t) = a+b*t
...
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2
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92
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Modelling exponential decay of a radioactive substance
Here is the problem I am struggling with. I can get the answer to part (a), but I couldn’t get the answer to part (b). I have attached an image showing the question and my working for part (b). If ...
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165
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Finding k in this logarithmic model
Problem 6: The amount of a certain medicine in the bloodstream decays exponentially
with a half-life of 5 hours. In order to keep a patient safe during a one-hour procedure,
there needs to be at ...
- 2,535
-1
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1
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Derivation of Exponential Model
A model for the mass of dye in the heart (mg) at any time from $t=2$ seconds until the end of the procedure: $H(t)=35e^{-0.916t}$
How was this derived?
The following information was used:
60% of ...
- 359
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2
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58
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why output values of linear transformation are wrong?
I am going to fit my data using an equation, Y=a*(1-e^(-bx))^c equation.
a & c are the intercept and slope, b is given.
Here are the steps I did:
...
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1
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1
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89
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Finding population growth rate given initial population and average pubs per female reproduction
I am new to mathematical modeling and having trouble modelling the following population growth scenario:
Starting population: $100$ individuals
Average age: $7$ years
Assumption: population equally ...
- 111
1
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3
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107
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How do Mathematicians determine when to use the constant $e$?
I'm only an undergrad so sorry if this is a dumb question, but I was studying Poisson distribution and it struck me that so many models involve "e". So it got me wondering; how/when/where/why do they ...
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628
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Mean time between failures for exponential distribution.
Let's say I have n independent machines that fail according to independent exponential distributions with mean of 1000 days. The machines can be shut down by the operator, so some of the samples we ...
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1
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39
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Exponential Modelling
Been asked a question and i can't seem to put it all together, i cant tell if there's not enough information or if i'm just being dumb.
A cup of hot milk cools from 100 degrees C cools to room ...
- 3
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77
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For given $a \in \mathbb{R}$ there exists unique continuous function $f:\mathbb{R} \to \mathbb{R}$. [duplicate]
For given $a \in \mathbb{R}$ there exists unique continuous function $f:\mathbb{R} \to \mathbb{R}$ that satiafy $f(x+y)=f(x)f(y)$ for $x,y \in \mathbb{R}$ and $f(1)=a$.
These theorems were discussed ...
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38
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How to mathematically introduce a function class of exponential decay?
I am not a mathematician so I need help with a correct mathematic definition/description of a function /function class that I will be using for modeling through curve fitting. The function describes ...
- 1
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1
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173
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Is it Possible to Linearise the Bounded Growth Model to use LLSQ?
At the moment I try to find the best (easiest) way to fit the bounded growth model
$$ y_i = a-ae^{bx_i},$$
with parameter $a,b∈ℝ$, and data points $(x_i,y_i)$. (This form is already simplified, ...
- 3,722
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1
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75
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Exponential Modelling; growth rate percentage to find length of cylindrical snake in regards to level number of snake game? [duplicate]
The problem I have is;
An app developer is creating a 3D snake game using a cylindrical model. Each time the snake grows, which occurs after it eats enough mice to level up and have a growth spurt, ...
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144
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Integral of the form $\int_{0}^{\infty}e^{-ax}e^{-x^{4}}dx$
I'm searching a closed form for the integral of the form :
$$
\int_{0}^{\infty}e^{-ax}e^{-x^\frac{\alpha}{2}}dx
$$
especially for $\alpha=8$
After several attempts, I find that the general form can ...
0
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2
answers
191
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How to model and solve this flower offerings to gods word problem?
So I came across this word problem and would like to get some help defining the model behind it and how to solve it.
There is a temple, whose premises have a garden and a pond. It has 4
idols, ...
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1
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22
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Is it possible to make a function of the form $A_1 e^{\frac{A_2}{\sqrt{x - A_3}}}$ converge to $B_1 e^{-B_2x}$ by using the correct constants?
There is a function $$ f_1 = B_1 e^{-B_2x} $$ where $B_1$ and $B_2$ are constants, and $x$ is a variable.
Is it possible to make a function of the form $$f_2 = A_1 e^{\frac{A_2}{\sqrt{x - A_3}}}$$ ...
- 613
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3
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228
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What are some clever (preferably physical) examples of processes exhibiting exponential growth?
My father is a high school STEM teacher and is pondering ideas for engineering projects where his students can model some type of physical process that demonstrates exponential growth.
One canonical ...
- 582
3
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1
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534
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When are Logistic Growth Models equivalent to exponential models?
When is the logistic growth model and exponential model equivalent?
Logistic Growth Model:
$P(1+t)=(P(t)*(-\frac b N )+1+b)*P(t)$
Where $b$ is the birth rate and $N$ is the Carrying Capacity.
...
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2
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366
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Approximation of a negative exponential model?
I am trying to get an approximation of this model, it is a negative exponential model introduced by Olson in 1963 "Energy storage and the balance of producers and decomposers in ecological systems". ...
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1
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38
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How to model function with unknown exponents?
I know the Cobb-Douglass function which describes the production quantity:
$$Q(K, L) = A \cdot K^\alpha \cdot L^\beta$$
Also I do know multiple assignments of K (...
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81
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relationship between two set of variable
i am trying to determine what kind of mathematical modeling could be applied following two variables,let us call them $x$ and $y$ ,namely change one variable has effect second on,i have several ...
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315
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How to define a surface $z = f(x,y)$ with flat region at centre and sigmoidally tapering towards the edges?
How do we define a continuos function $f(x,y)$ within the bounded domain $x \in [a,b]$ and $y \in [c,d]$ so that $z=f(x,y)$ has a flat surface at the centre (flat means $f(x,y)= C$, $C$ being ...
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1
answer
1k
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exponential population growth models using $e$?
Im trying to understand this write up [1] of cell population growth models and am confused about the use of natural logarithms. If cells double at a constant rate starting from 1 cell, then their cell ...
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