How Do You Model Desert Temperature Variations Mathematically?

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Homework Help Overview

The problem involves modeling daily temperature variations in a desert environment, specifically oscillating temperatures between 40 degrees F and 80 degrees F over a 12-hour period. The task is to formulate a mathematical expression for temperature as a function of time measured in hours from 5 am.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss potential formulas for the temperature function, examining sine and cosine functions. There is a focus on amplitude and period, with questions about the correctness of the initial attempts and the need for adjustments based on the starting temperature.

Discussion Status

Some participants have provided feedback on the original poster's attempts, suggesting that the amplitude and period may need reconsideration. There is an ongoing exploration of different mathematical representations, but no consensus has been reached regarding the final formula.

Contextual Notes

Participants are working within the constraints of the problem statement, which specifies the temperature range and the time frame for oscillation. There is an indication that the original poster may have misunderstood the implications of amplitude in their initial formulation.

Quantum_Grid
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Homework Statement


The desert temperature, H, oscillates daily between 40 degrees F at 5 am, and 80 degrees F at 5 pm. Write a possible formula for H in terms of t, measured in hours from 5 am.


The Attempt at a Solution


The best I can come up with is

H=60+40sin((pi/6)t)

but this does not look right when I try and graph it on a calculator. I think the 40sin part is what I have wrong, but I cannot figure out what goes there, and the book is no help at all. Am I at least close?
 
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The amplitude of the oscillation is 40, but multiplying the base function by 40 will make it oscillate between -40 and 40, giving it an amplitude of 80. Ie., your function oscillates between 60 - 40 = 20 and 60 + 40 = 100.
 
OK, I looked a little closer and I think they want it to start at 40. So I got H=60+(-20)cos((pi/12)t)

I think I had the period wrong too... This looks right...right?
 
Quantum_Grid said:
OK, I looked a little closer and I think they want it to start at 40. So I got H=60+(-20)cos((pi/12)t)

I think I had the period wrong too... This looks right...right?

Looks great!
 

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