Question

The number of blogs (or weblogs) grew rapidly for several years. According to one report, there were about 2 million blogs in March 2004, after which the number of blogs doubled approximately every six months. Note: Growth tapered off after 2007, and at the end of 2011 there were about 175 million blogs. Let N denote the number (in millions) of blogs and d the number of doubling periods after March 2004. Use a formula to express N as an exponential function of d.

Answer 1

Answer:

$N(d)=2e^{0.32d}$

Step-by-step explanation:

Because the growth rate is not constant (as it changes after 2007), then we must find an average rate to use the continue exponential growth function which is given by:

$N(d)=N_{0}e^{rd}$

Where,

d: number of periods

N(d): total number of blogs in d periods (in millions).

$N_{0}:$: total number of blogs on the initial period (in millions)

r: average growth rate (this is the one we must find)

With the given information we may consider that:

d=14  The reason for this is that between March 2004 to March 2011 there are 7 years with 14 periods of 6 months(2x7).

N=175 (millions)

$N_{0}=2$ (millions)

Therefore,

$175=2e^{14r}$

We find r by solving the equation above:

$\frac{175}{2}=e^{14r}$

$Ln\frac{175}{2}=14r$

$r=\frac{Ln(175/2)}{14}=0.32$

Therefore our formula is as it follows:

$N(d)=2e^{0.32d}$