Chapter 16.2, Problem 72E

To determine

To calculate: The value of eccentricity $200,000$ years ago and rate at which it was changing if the eccentricity of the Earth`s orbit (the deviation of the Earth`s orbit from a perfect circle) can be modeled by the equation $E\left(t\right)=0.025\left[\cos \left(\frac{2\pi \left(t+200\right)}{400}\right)\right]+\cos \left(\frac{2\pi \left(t+200\right)}{100}\right)$ where $E\left(t\right)$ is the eccentricity and t is time in thousands of years, with $t=0$ being the present time.