In country a, the number of highway bridges for the years 2000 to 2005 can be modeled by the equation y=149(x+1.5)^2+489,505, where x=0 represents the year 2000. assume that this trend continued and find the year in which there were 505,000 highway bridges in country a.

Given that the number of bridges has been modeled by the function:
y=149(x+1.5)^2+489,505
To find the year in which, y=505000 we shall proceed as follows:
From:
y=149(x+1.5)^2+489,505
substituting y=505000 we shall have:
505000=149(x+1.5)^2+489,505
simplifying the above we get:
0=149(x+1.5)^2-15495
expanding the above we get:
0=149x^2+447x+335.25-15495
simplifying
0=149x^2+447x-15159.8
solving the quadratic equation by quadratic formula we get:
x~8.69771 or x~-11.6977
hence we take positve number:
x~8.69771~8.7 years~9 years
thus the year in which the number will be 505000 will be:
2000+9=2009