Final answer:
To find the predicted population in 2007 and 2010, we need to substitute the corresponding values of x into the given function y = 15,000 + 4,000 sin(0.637x). For x = 2007 - 1980 = 27, the predicted population in 2007 is 18,600. For x = 2010 - 1980 = 30, the predicted population in 2010 is 18,223.
Step-by-step explanation:
To find the predicted population in 2007 and 2010, we need to substitute the corresponding values of x into the given function y = 15,000 + 4,000 sin(0.637x).
For x = 2007 - 1980 = 27:
y = 15,000 + 4,000 sin(0.637 * 27) = 15,000 + 4,000 sin(17.199) = 15,000 + 3,600 = 18,600.
So, the predicted population in 2007 is 18,600.
For x = 2010 - 1980 = 30:
y = 15,000 + 4,000 sin(0.637 * 30) = 15,000 + 4,000 sin(19.11) = 15,000 + 3,223 = 18,223.
So, the predicted population in 2010 is 18,223.