1. Mitochondria are organelles that provide energy for human and other eukaryotic cells. Mitochondria can divide like bacteria and fuse with each other. Use the following assumptions to write a differential equation for M, the number of mitochondria in a cell.
   1. a) There is an optimal mitochondrial population, m. The rate at which mitochondria reproduce is proportional to the difference between the current population and the optimal population, with propor- tionality constant r.
   2. b) When two mitochondria are close to one another, they may fuse together. This occurs with probability f .
   3. c) Mitochondria die at a constant per-capita rate d.