Outside temperature over a day can be modeled as a sinusoidial function. Suppose

Question

Outside temperature over a day can be modeled as a sinusoidial function. Suppose you know the high temperature for the day is 96 degrees and the low temperature of 64 degrees occurs at 4am. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t Outside temperature over a day can be modeled as a sinusoidial function. Suppose you know the high temperature for the day is 96 degrees and the low temperature of 64 degrees occurs at 4am. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t

Explanation / Answer

comparing with D(t)= Asin(B(t+C)) +k

high temperature for the day is 96 degrees and the low temperature of 64 degrees

A=(96-64)/2

A=16

k=(96+64)/2

k=80

period =24 hours

2/B =24

=>B= /12

D(t)= 16sin(( /12)(t+C)) +80

4 am is 4 hours from midnight , low temperature of 64 degrees occurs at 4am

D(4)=64

=> 16sin(( /12)(4+C)) +80=64

=> 16sin(( /12)(4+C)) =-16

=>sin(( /12)(4+C)) =-1

=>(( /12)(4+C)) =-/2

=>(4+C) =-6

=>C=-10

so function is  D(t)= (16*sin(( /12)*(t-10))) +80 or you can use D(t)= 16sin(( /12)(t+14)) +80

please rate if helpful. please comment if you have any doubt

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