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

Answer 2

Using a system of equations, it is found that the function is given by:

$y = \frac{x^2}{160} + \frac{x}{8} + 20$

The standard format of a quadratic equation is given by:

$y = ax^2 + bx + c$

Initial price of $20, thus $c = 20$. Then:

$y = ax^2 + bx + 20$

After 20 days, price of $30 per share, thus when $x = 20, y = 30$, then:

$30 = a20^2 + 20b + 20$

$400a + 20b = 10$

After 40 days, price of $35 per share, thus when $x = 40, y = 35$, then:

$35 = a40^2 + 40b + 20$

$1600a + 40b = 15$

Then, the system is:

$400a + 20b = 10$

$1600a + 40b = 15$

Multiplying the first equation by 2, and subtracting by the second:

$800a + 40b = 10$

$1600a + 40b = 15$

$-800a = -5$

$a = \frac{5}{800}$

$a = \frac{1}{160}$

Then

$40b = 10 - 800a$

$40b = 10 - \frac{800}{160}$

$40b = 5$

$b = \frac{1}{8}$

Thus, the equation is:

$y = \frac{x^2}{160} + \frac{x}{8} + 20$

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