What type of mathematical function is this? Thanks :)

Hawaiianboi808
Messages
1
Reaction score
0
John lives in Dallas and his kitchen has a room temperature of about 70 degrees fahrenheit. He wanted to make her family some cookies for dessert, so he preheated her oven to 350 degrees fahrenheit. In 1 minute, the oven was 135 degrees fahrenheit. In 2 minutes, the oven was about 200 degrees fahrenheit. In 4 minutes, it went up to about 300 degrees fahrenheit. John's cookie dough was ready to go in the oven about 10 minutes after he turned it on.

I believe that this is an exponential function. Not sure, please double check.

Include example of formula.

Thank you
 
Mathematics news on Phys.org
We could likely model this with a function of the form (which comes from Newton's Law Of Cooling):

$$f(t)=c_1e^{-kt}+350$$

Since we know $f(0)=70$, we then have:

$$f(t)=-280e^{-kt}+350$$

And we know $f(1)=135$, so we have:

$$f(t)=-280\left(\frac{43}{56}\right)^t+350=70\left(5-4\left(\frac{43}{56}\right)^t\right)$$

This doesn't fit the remaining points exactly, but it is the type of function we would expect. :D
 
If you want to exactly fit all points, given any n points, there exist a polynomial of degree n-1 that passes through each of those points. Here, there are three points, (1, 135), (2, 200), and (4, 300) so there exist a quadratic polynomial that passes through the three points.

Any quadratic polynomial can be written in the form y= ax^2+ bx+ c. The data above gives 135= a+ b+ c, 200= 4a+ 2b+ c, and 300= 16a+ 4b+ c. Solve those three equations for a, b, and c.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

Similar threads

Replies
13
Views
3K
Replies
6
Views
4K
Replies
1
Views
2K
Replies
1
Views
3K
Replies
1
Views
3K
Replies
1
Views
3K
Replies
7
Views
3K
Back
Top