#### Answer

122

#### Work Step by Step

According to the data in the question 'If $x$ is the time in years, with $x = 0$ representing January 1 of the base year, $x=0.5$ representing July 1 of the same year and $x=1.75$ representing October 1 of the following year'. This means that $x=1$ represents January 1 of the following year.
Therefore, we substitute $x=1$ in the equation to find the pollution level y on the aforementioned date:
$y=7(1-\cos2\pi x)(x+10)+100e^{0.2x}$
$y=7[1-\cos2\pi (1)](1+10)+100e^{0.2\times1}$
$y=7(1-\cos 2\pi)(11)+100e^{0.2}$
$y=7(1-1)(11)+100(1.22140)$
$y=7(0)(11)+122.140$
$y=0+122.14$
$y=122.14\approx122$
Therefore, the pollution level on January 1 of the following year is 122.