SOLUTION: The revenue R (in millions of dollars) of a large retail store can be modeled by R=1.23t^2-2.22t+8.5, where t is the number of years since 1990. Estimate the year in which the stor

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The revenue R (in millions of dollars) of a large retail store can be modeled by R=1.23t^2-2.22t+8.5, where t is the number of years since 1990. Estimate the year in which the stor      Log On


   

Question 139631: The revenue R (in millions of dollars) of a large retail store can be modeled by R=1.23t^2-2.22t+8.5, where t is the number of years since 1990. Estimate the year in which the store's revenue will reach 90 million dollars?
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Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The revenue R (in millions of dollars) of a large retail store can be modeled by R=1.23t^2-2.22t+8.5, where t is the number of years since 1990. Estimate the year in which the store's revenue will reach 90 million dollars?
:
Replace R with 90 and solve for t
1.23t^2 - 2.22t + 8.5 = 90
:
1.23t^2 - 2.22t + 8.5 - 90 = 0
:
1.23t^2 - 2.22t - 81.5 = 0
:
Use the quadratic formula:x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation: a=1.23, b=-2.22, c=-81.5
t+=+%28-%28-2.22%29+%2B-+sqrt%284.9284+-+4+%2A+1.23+%2A+-81.5+%29%29%2F%282%2A1.23%29+
:
t+=+%282.22+%2B-+sqrt%284.9284+-+%28-400.98%29+%29%29%2F%282.46%29+
:
t+=+%282.22+%2B-+sqrt%284.9284+%2B+400.98+%29%29%2F%282.46%29+
:
t+=+%282.22+%2B-+sqrt%28405.9084+%29%29%2F%282.46%29+
Positive solution
t+=+%282.22+%2B+20.147%29%2F2.46
t = 22.367%2F2.46
t = 9.09 ~ 9 yrs; 1999 is the year of 90 million dollars