Question

Dingane has been observing a certain stock for the last few years and he sees that it can be modeled as a function S(t)S(t)S, left parenthesis, t, right parenthesis of time ttt (in days) using a sinusoidal expression of the form a\cdot\sin(b\cdot t)+da⋅sin(b⋅t)+da, dot, sine, left parenthesis, b, dot, t, right parenthesis, plus, d. On day t=0t=0t, equals, 0, the stock is at its average value of {\$}3.47$3.47dollar sign, 3, point, 47 per share, but 91.2591.2591, point, 25 days later, its value is down to its minimum of \$1.97$1.97dollar sign, 1, point, 97. Find S(t)S(t)S, left parenthesis, t, right parenthesis. \textit{t}tstart text, t, end text should be in radians.

Answer 1

-1.5sin(2π/365*t)+3.47

Explanation:

Answer 2

S(t) = 1.5 sin(πt/60.83) + 3.47

Explanation:

S(t) = a.sin(b.t) +d

Average value at 0 day = 3.47

Therefore d = 3.47

with t at 91.25 days, the value is down it minimum = 1.97

i.e. d - a = 1.97

a = d - 1.97

= 3.47 - 1.97

a = 1.5

at t = 91.25

bt = 3π/2

b= 1.5
`\pi`/t

b = 1.5
`\pi`/91.25

b =
`\pi`/60.83

S(t) = 1.5 sin(πt/60.83) + 3.47