Question

A group of scientists found a new species of spider in the desert. The body temperature of the spider appears to vary sinusoidal over time. A maximum body temperature of the spider reaches 125° after 15 minutes from the start of the examination. Then, 28 minutes later, the body temperature falls to a minimum of 99°. The scientists would like to write an equation to model the body temperature of the spider over time. Which function will model their findings?
a.) f(t)=13sin(2pi/28)*(t-1)+112
b.) f(t)=13sin(pi/28)*(t-1)+112
c.) f(t)=13sin(pi/56)*(t-1)+112
d.) f(t)=26sin(pi*t/28)+112

How do I calculate Amplitude, period, etc. to find a function? I think that the correct answer is c, but I'm not positive. Thanks!

Answer 1

amplitude is half the distance between the extremes. In this case, (125-99)/2 = 13

The midline (where sin(x) = 0) is (125+99)/2 = 112

The period is twice the time from max to min, or 28*2 = 56

So, we're looking at something like

y=13 sin(pi/28 t)+112

Now for the phase shift. The max was at t=15, so y=0 at t=1, 1/4 period earlier.

y=13 sin(pi/28 (t-1))+112

that is, choice (b)

see the graph at

http://www.wolframalpha.com/input/?i=%3Dsin%28%28pi%2F28%29*%28x-1%29%29

Answer 2

It goes from 125 to 99 in 28 minutes, so a whole cycle or a period would be 56 minutes

period = 2π/k = 56
k = 2π/56 = π/28
which automatically rules out a) and c)

The sin(anything) has a max of 1 and a min of -1
so 13+112 = 125
-13+112 = 99
So a), b), and c) have that property, ruling out d)

(unless none of them are correct, b) is it )

let's test it for the given values:
if t = 15, we should get 125
temp = 13sin(π/28)(15-1) + 112
= 13 sin (14π/28) + 112 = 13(1) + 112 = 125 , ok!
if t = 43, we should get 99
temp = 13sin (π/28)(43-1) + 112
= 13 sin (3π/2) + 112 = 13(-1) + 112
= 99, OK!!

so b)

Answer 3

Thanks SO much!!