Claude is reading a science fiction book in which aliens have dropped a fungus on a 10 square mile section of a planet. The fungus spreads rapidly, increasing the area it covers by 50% every hour. The total area of the planet is 200 million square miles. Claude created an equation and determined that it will take approximately 41 hours for the fungus to cover planet. What is the equation that Claude created?

"curse these trig-loving pirates! " devora mutters as she looks at the map. then, after thinking for a moment, she walks back to the entrance of the secret cave, measuring 48 meters along the way. after performing a calculation, devora walks back to the empty treasure, faces the entrance, and turns a certain number of degrees to her left before walking 89 meters to the treasure. supposing that the angle at the cave entrance is acute and that devora's calculations were correct, how many degrees did she turn?