The researchers have also determined that the current rate of the rise in water level is twice the 1880 to 2009 rate. assuming that this new rate began in 2009, you can use the function g(x) = 3.2(x - 2009) + 206, which models the total rise in water level in mm since 1880 for any year x, beginning in 2009.

1. what is the domain of g(x)?
2. write a simplified function, g(x)
3. according to the model, what will be the total rise in water level by 2025?
4. when will the total rise in water level be equal to about half a meter?

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Step-by-step explanation:

1. The problem statement tells you the function applies for year values (x) 2009 and later. The domain is real numbers greater than or equal to 2009.

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2. We can use the distributive property to eliminate parentheses:

  3.2(x -2009) +206 = 3.2x -6428.8 +206

  = 3.2x -6222.8

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3. Put 2025 in the equation and do the arithmetic

  g(2025) = 3.2·2025 -6222.8 = 257.2 . . . . mm

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4. Put this value of level rise in the equation and solve for x.

  g(x) = 3.2x -6222.8

  500 = 3.2x -6222.8 . . put 500 mm where g(x) is in the equation

  6722.8 = 3.2x . . . . . . . add 6222.8

  x = 6722.8/3.2 = 2100.875

The water rise will be equal to about half a meter late in the year 2100.