Chapter 16.2, Problem 71E

(a)

To determine

To calculate: The function that best models the tilt of the Earth's axis if the tilt of the Earth's axis from its plane of rotation about the sun oscillates between approximately $22.5°$ and $24.5°$ with a period of approximately $40,000$ years and $500,000$ years ago, the tilt of the Earth's axis was $24.5°$ where $A\left(t\right)$ is the tilt in degrees and t is time in thousands of years, with $t=0$ being the present time.

(b)

To determine

To calculate: The rate at which the tilt was changing $150,000$ years ago using the model from part (a), if the tilt of the Earth's axis from its plane of rotation about the sun oscillates between approximately $22.5°$ and $24.5°$ with a period of approximately $40,000$ years and $500,000$ years ago, the tilt of the Earth's axis was $24.5°$ where $A\left(t\right)$ is the tilt in degrees and t is time in thousands of years, with $t=0$ being the present time.