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.

Question

Amirah Mendez

Mathematics

11 February, 06:38

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.

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Rodney Horn · 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