Question

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.

Answer 1

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