Question

The initial price of buzz stock is $20 per share. After 20 days the stock price is $30 per share and after 40 days the price is $35 per share. Assume that while the price of the stock is not zero it can be modeled by a quadratic function. (a) Find the multipart function s(t) giving the stock price after t days.

Answer 1

Answer:

$s(t) = -\dfrac{t^2}{160}+\dfrac{5}{8}t+20$

Step-by-step explanation:

given,

initial price of buzz stock = $ 20 per share

after 20 days

stock price = $30 per share

after 40 days

the price =  $35 per share

let say it is modeled by

y = ax² + b x + c

x = number of days

y = stock price

x = 0 y = 20

20 = a x 0 + b x 0 + c

c = 20

x = 20 y = 30

30 = 20² a + 20 b + 20

400 a + 20 b = 10...........(1)

x = 40 y = 35

35 = 40² a + 40 b + 20

1600 a + 40 b = 15...........(2)

solving equation (1)and (2)

a = - 1/160

b = 5/8

$y = -\dfrac{x^2}{160}+\dfrac{5}{8}x+20$

$s(t) = -\dfrac{t^2}{160}+\dfrac{5}{8}t+20$

hence , the above equation is multipart function