Chapter 4.1, Problem 18E

Reminder Round all answers to two decimal places unless otherwise indicated.

Internet Domain Hosts Often new technology spreads exponentially. Between $1995$ and $2005$, each year the number of Internet domain hosts was $1.43$ times the number of hosts in the preceding year. In $1995$, the number of hosts was $8.2\text{ million}$.

a	Explain why the number of hosts is an exponential function of time.
b	Find the formula for the exponential function that gives the number $N$ of hosts, in millions, as a function of the time $t$ in years since $1995$.
c	According to this model, in what year did the number of hosts reach $24\text{ million}$.