A company analyzed its stock price for the period 2002 to 2010 and modeled the price as a polynomial given by p(t) = t3 – 12t2 + 32t + 50, where p is the stock price (in dollars) and t is the number of years passed since January 1, 2002. In which period will the stock price be lower than $50?

QUESTION POSTED AT 29/05/2020 - 01:11 AM

Answered by admin AT 29/05/2020 - 01:11 AM

Given that the stock price of a given company over a period of 8 years can be modeled by P(t)=t^3-12t^2+32t+50. Where p is the price and t is the number of years passed.
To get the period whereby the stock price will be less than $50 we proceed as follows;
First we find the derivative of the function;
thus solving for t we get;
t=6.31 or 1.69
Evaluating the values of p at this point we get:
Evaluating the point before  and after t=1.69 say t=0 and t=3 we get:
Evaluating the point immediately before and after t=6.31 say t=6 and t=7
from the above we see that the lowest point was at point t=6.31, thus the time period when t was below $50 was at the interval t=0 and t=6.31

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