At the beginning of 2006 Facebook membership was 5.5 million, and at the beginning of 2008 the membership had increased to 58 million.

Question

1. (a) Assume that the membership increases exponentially, and find an exponential growth model for Face- book membership. Let t be the time in years with t = 0 in 2006 and F(t) the number of Facebook members in millions at time t.
2. (b) Use your model to estimate Facebook membership in 2018.
3. (c) What is Facebook membership in 2018? (Google it.) How well does your estimate in (b) compare with this number?

Answer 1

5.5 = 5.5e^rt t=0

58 =5.5e^2r

r= .5ln(58/5.5)

in 2018 t=12

every 2 years pop increases by factor of 10.545454= 58/5.5

in 6 2 year periods= 12 years..

f(x)=5.5(58/5.5)(6)= 348 million in 2018

actual: 220 million

huge overestimate