**Question: **The forthcoming zombie apocalypse can be modeled with the differential equation \(\frac{dP}{dt}=kP\). On the 21st of the apocalypse, the number of zombies is 114,848. On the 40th day, the number of zombies has increased to 29,428,100.

a) Assuming unlimited growth, find the general equation P(t).

b) How many zombies were there on day (t=)0?

c) How many days will it take to overcome the entire U.S. population of 313 million?

d) How many days will it take to overcome the entire global population of 7billion?