## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 4 - Graphs of the Circular Functions - Section 4.1 Graphs of the Sine and Cosine Functions - 4.1 Exercises - Page 151: 55c

#### Answer

In $L(x)$, we can see the quadratic function: $0.022x^2+0.55x+316$ As $x$ increases, the quadratic function causes $L(x)$ to show an increasing trend in general. This increase could be caused by the burning of fossil fuels. In $L(x)$, we can see the sine function: $3.5~sin~2\pi x$ Within each year, the sine function reflects the seasonal increase and decrease of carbon dioxide levels. During the summer, plants absorb large amounts of carbon dioxide from the atmosphere. This carbon dioxide is released into the atmosphere again at the end of the fall and during the winter.

#### Work Step by Step

$L(x) = 0.022x^2+0.55x+316+3.5~sin~2\pi x$ In $L(x)$, we can see the quadratic function: $0.022x^2+0.55x+316$ As $x$ increases, the quadratic function causes $L(x)$ to show an increasing trend in general. This increase in the carbon dioxide level each year could be caused by the burning of fossil fuels which releases large amounts of carbon dioxide into the atmosphere each year. In $L(x)$, we can see the sine function: $3.5~sin~2\pi x$ Within each year, the sine function reflects the seasonal increase and decrease of carbon dioxide levels. During the summer, plants absorb large amounts of carbon dioxide from the atmosphere, which results in a decrease in the carbon dioxide level in the atmosphere during the summer. This carbon dioxide is released into the atmosphere again at the end of the fall and during the winter, resulting in an increase in the level of carbon dioxide in the atmosphere.

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