Algrebra unit 7

Question

Temperature of math like for one day is show on the graph to the right. What is the amplitude? What is the period? Write the equation that models the temperature. Find f(6) . Use a sentence to explain what it means.

time (hours since 8:00)

Answer 1

f(6)= temperature at 4 am in the morning, probably about the minimum

amplitude =max temp- average temp = A=max-D=

= average -minimum temp= D-f(6)

max = D+f(6) at about 4pm

average=D about 10pm and 10 am when t =2, 14, 26, 38,...

period = the cycle time, time when the temp repeats

= 24 hours= 1/frequency =24B/pi

f(t)=Asin(Bt-C)+D

A=Amplitude=(max-min)/2

D= average temp=(max+min)/2

C=phase shift=0

B(2)-C= 2pi

B=pi,

f(t)=Asin(pi(t)) +D

= Acos(pi(t) +pi/2)+D

you can model it with either sine or cosine wave,

but with a different phase shift

Still same amplitude, period and mean, either way