Between 2000 and​ 2005, the number of skateboarders s in the United​ States, in​ millions, can be approximated by the equation s=0.33t^2+2.27t+3.96 where t represents the number of years since 2000.

Question

If this model is​ accurate, in what year did 9.8 million people​ skateboard? Round to the nearest whole number.

Answer 1

s = 0.33t^2 + 2.27t + 3.96 = 9.8, solve for t

0.33t^2 + 2.27t - 5.84 = 0

t = (-b +- sqrt(b^2 - 4ac)) / 2a

b^2 - 4ac = 2.27^2 + 4*0.33*5.84 = 12.86

t = (-0.33 +- sqrt(12.86) ) / 2*0.33 = ( -0.33 +- 3.59 ) / 0.66

We need to positive solution

t ~ 5 years from 2000 so 2005