Explanation:
To predict sales for June 2011, we need to substitute the corresponding value of t into the given sales forecast equation:
t = (month number in June 2011 - month number in January 2010) = (18 - 5) = 13
Now, let's calculate the sales (s) for June 2011:
s = 2.31 + 0.442t + 4.3 * cos(pi * t / 6)
s = 2.31 + 0.442 * 13 + 4.3 * cos(pi * 13 / 6)
s = 2.31 + 5.746 + 4.3 * cos(13pi / 6)
Note: pi is approximately equal to 3.14159.
Now, we need to calculate the cosine value:
cos(13pi / 6) ≈ cos(2.16667 * pi) ≈ cos(2 * pi - 0.975) ≈ cos(0.975) ≈ 0.549
Now, let's calculate the sales (s) for June 2011:
s ≈ 2.31 + 5.746 + 4.3 * 0.549
s ≈ 8.056 + 2.3567
s ≈ 10.412
Therefore, the predicted sales for June 2011 would be approximately 10.412 thousand units. Rounded to three decimal places, the prediction is 10.412.