Question 555297
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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