“Night Comes to the Cretaceous” and other tales of the decibel

This education paper presents three entertainment problems that may be of use to educators. These problems illustrate how to use the decibel scale for back of the envelope calculation without a calculator. "Night Comes to the Cretaceous" estimates the size the meteor believed to have caused the extinction of the dinosaurs from the diameter of the Chicxulub crater in the Yucatan, the crater excavated by the detonation of the first hydrogen bomb, and the radius of the Earth's orbit around the Sun. "Euler Would Be Proud" shows how to easily determine powers of e and how to determine natural logarithms without a calculator. "The Amazing Number 1.6" demonstrates that the doubling of the number of transistors on a chip every 18 months of Moore's Law corresponds to an annual compound growth rate of 60% and then shows the implications of this growth rate on computational power over periods of decades. This paper uses the by-hand rational approximations to the multiplicative factors corresponding to integer decibel values between 1 and 20 and the rational decibel approximations corresponding to integer factors between 1 and 10 that appeared in [2].