How Do You Model Desert Temperature Variations Mathematically?

[Quantum_Grid]

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?

 

[slider142]

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.

 

[Quantum_Grid]

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?

 

[slider142]

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!