SOLUTION: The total number S (in millions) of sheep and lambs on farms in a country from 1995 through 2002 can be approximated by the model S = 0.032t^2 − 0.87t + 12.6, 5 ≤ t ≤ 12

Question 1190250: The total number S (in millions) of sheep and lambs on farms in a country from 1995 through 2002 can be approximated by the model
S = 0.032t^2 − 0.87t + 12.6, 5 ≤ t ≤ 12,
where "t" represents the year, with t = 5 corresponding to 1995. Use a graphing utility to graph the model. Extend the model past 2002. Does the model predict that the number of sheep and lambs will eventually increase? If so, estimate when the number of sheep and lambs will once again reach 8 million.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
S = 0.032t^2 − 0.87t + 12.6, 5 ≤ t ≤ 12,

The minimum point is where t=-b/2a or 0.87/0.064=13.59 years or sometime in 2008. Within the range of t, the number will stay below 8 million.
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If you want to show outside the original domain when 8 would be reached,
this would be a quadratic with 0.032t^2-0.87t+4.6=0, and t=20 or in 2015 when y= exactly 8. It does predict when the number will increase pass 8 million. Whether early or late 2015 depends upon when in 1990 the original 0 was set.
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