Chapter 10.1, Problem 18E

According to a $\text{September 9, 2007}$, article in ZDNet, the number of Facebook users “is growing at $3$ to $4$ percent compounded weekly, with about $\text{38 million}$ members currently.”

a. Why does this statement imply exponential growth?

b. Use these data (and a $3.5\%$ weekly growth rate) to develop the exponential growth model for the number of users, where t is the number of weeks after $\text{September 9, 2007}$

c. Use the model to predict the number of Facebook users in the first week of $\text{January 2011}$.

d. The article goes on to say that “In three years, we could have everybody on the planet, but that's not going to happen.” Discuss why it's not going to happen and what this means about using an exponential model to make predictions.