The mythical Hydra was a beast that was very difficult to kill -- if you cut off its head, it grew 12 new ones to replace it. If you cut off one of those heads, 12 more would grow... if you cut off one of those, 12 more would grow ....
The mythical Super-Hydra is even worse -- cutting off the one head causes 12 more to grow, but cutting off one of the new heads causes all of them to die! For an instant... and then ALL 12 OF THEM SPROUT 12 NEW HEADS!
- Write equations describing the number of heads as a function of the number of times you've cut off a head for both the regular Hydra and the Super-Hydra.
2. How many heads would you have to cut off before each Hydra gets to 1 BILLION heads? Use the equations in 1 to solve without using guess and check.