Need Math help exponents/logarithms word problem

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To determine how long a gallon of milk lasts at 30 degrees Celsius, the problem requires fitting the given data points (0, 192) and (22, 42) to a mathematical function. The initial attempt involved using logarithmic equations, but it did not yield a suitable solution. Participants emphasized the need for clarity in the problem description to apply the correct mathematical approach. A suggestion was made to consider a linear equation for the data fitting. The discussion highlights the importance of providing complete information for effective problem-solving.
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Homework Statement


A gallon of milk will last 192 hours at 0 degrees celcius, 42 hours at 22 degrees celcius, how long will it last at 30 degrees celcius?


Homework Equations





The Attempt at a Solution

 
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What have you tried? You need to show some effort at a problem before anyone can help you. Them's the rules...
 
Log (H) = 192 - Log (T)^x

Fits for the first data set, but doesn't fit the problem?

I'm confused and stuck?
 
You have not given us the entire problem description. Apparently you are supposed to fit this data to some kind of function. Since you are given two points-- (0, 192) and (22, 42), one possibility is to fit this data to a linear equation.

If you are supposed to do this some other way, please specify what that way is.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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