Chapter 2, Problem 93RE

Medicine. One leukemic cell injected into a healthy mouse will divide into $2$ cells in about $\frac{1}{2}$ day. At the end of the day these $2$ cells will divide into $4$. This doubling continues until $1$ billion cells are formed; then the animal dies with leukemic cells in every part of the body.

(A) Write an equation that will give the number $N$ of leukemic cells at the end of $t$ days.

(B) When, to the nearest day, will the mouse die?