Answer:
[tex][/tex] 34$,46$
Step-by-step explanation:
To find the time and value when the stock prices are the same, we can set the two equations for the stock prices equal to each other and solve for t:
C -t² + 12t + 14 = 2t + 30
Rearranging the equation gives us:
-t² + 12t - 2t = 30 - 14
Combining like terms:
-t² + 10t = 16
This equation is a quadratic equation, and we can solve for t using the quadratic formula:
t = (-b ± √(b² - 4ac)) / (2a)
Here, a = -1, b = 10, and c = -16. Plugging these values into the quadratic formula, we get:
t = (-10 ± √(10² - 4(-1)(-16))) / (2(-1))
t = (-10 ± √(100 - 64)) / (-2)
t = (-10 ± √36) / (-2)
t = (-10 ± 6) / (-2)
So we have two potential solutions:
t = (-10 + 6) / (-2) = -4 / (-2) = 2
t = (-10 - 6) / (-2) = -16 / (-2) = 8
The stock prices are the same at 2 years and 8 years.
To find the value of the stock prices at the time when they are the same, we can substitute the value of t back into either equation. Let's use the second high-tech stock's price equation C = 2t + 30:
C = 2 2 + 30 = 4 + 30 = 34
C = 2 8 + 30 = 16 + 30 = 46
So, the stock prices are the same at 2 years and 8 years, with the value being $34 and $46 per share, respectively.
