Question 555297: It is estimated that t years from now the population of a particular city will be....
P = t^2 - 24t + 96,000
How many years from now will the population be 95,865?
Thanks in advance, I appreciate it!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! P = t^2 - 24t + 96000
95865 = t^2 - 24t + 96000
0 = t^2 - 24t + 96000 - 95865
0 = t^2 - 24t + 135
Now use the quadratic formula to solve for t:
t = (-b+-sqrt(b^2-4ac))/(2a)
t = (-(-24)+-sqrt((-24)^2-4(1)(135)))/(2(1))
t = (24+-sqrt(576-(540)))/(2)
t = (24+-sqrt(36))/2
t = (24+sqrt(36))/2 or t = (24-sqrt(36))/2
t = (24+6)/2 or t = (24-6)/2
t = 30/2 or t = 18/2
t = 15 or t = 9
So this means that in 15 or 9 years the population will be 95,865
Note: the population will reach 95,865 in 9 years first, dip below 95865 and then climb back up to 95,865 when t = 15
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Jim
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