# Chapter 4 - Review Exercises - Page 192: 53a

100

#### Work Step by Step

According to the question, January 1 of the base year is represented by $x=0$. Therefore, we substitute $x=0$ in the equation to find the pollution level y on the aforementioned date: $y=7(1-\cos2\pi x)(x+10)+100e^{0.2x}$ $y=7[1-\cos2\pi (0)](0+10)+100e^{0.2\times0}$ $y=7(1-\cos 0)(10)+100e^{0}$ $y=7(1-1)(10)+100(1)$ $y=7(0)(10)+100(1)$ $y=0+100$ $y=100$ Therefore, the pollution level on January 1 of the base year is 100.

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