Zombie Dogs Attack!

An extra credit assignment for my calculus class:
A pack of zombie dogs (ZDs) is reproducing quickly and killing humans. Scientists and calculus students have determined that the the total number of human deaths due to ZDs t days after the start of 2010 is given by

1. At the end of January 1st (t = 1), how many deaths have occurred?

2. At the end of January, how many deaths will have occurred?

3. Determine the number of deaths/day after t days: h′(t).
Hint: you may want to go “outside-in” with the chain rule.

4. Graph both h(t) and h'(t) on the same axes:

5. On what day will 90% of the human population (6.8 billion) be annihilated by ZDs?

6. When does the death rate reach half a billion per day?

7. When does the death rate hit its peak?