Question 223606
I assume you meant t^2 rather than r^2? If not let me know...
{{{P=-4t^2+80t-360}}}
P is the price, so set the equation equal to 24:
{{{24=-4t^2+80t-360}}}
Equate quadratic to zero:
{{{-4t^2+80t-384=0}}}
You can factor this:
{{{(2t-24)(-2t+16)=0}}}
Equate each term to zero and solve for t:
{{{2t-24=0}}}
{{{2t=24}}}
{{{highlight(t=12)}}}
{{{-2t+16=0}}}
{{{-2t=-16}}}
{{{highlight(t=8)}}}
To get the actual months where the stock was $24, remember that January 2003 is 1. So you can see that the stock was at this price in August and December of 2003.
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Good Luck,
tutor_paul@yahoo.com