Davis notices that his hair is decreasingly exponentially at a rate of 10% per year. if he starts with 100,000 on his head, how many will he have after 3 years?

You are standing next to a really big circular lake. you want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! you decide to walk around the perimeter of the lake and measure its circumference, and find that it's 400\pi\text{ m}400? m. what is the diameter dd of the lake?