1. The US Dept of Commerce estimates that the number of internet users worldwide
ID: 3138296 • Letter: 1
Question
1. The US Dept of Commerce estimates that the number of internet users worldwide was 2.2 billion in 2011 and 2.9 billion in 2014.
(a) Find an exponential model f for this data in which t is measured in years, with t=0 corresponding to 2011, and f(t) is measured in billions. Round b to three decimal places.
(b) Use the results of part (a) to determine f(4). Interpret your answer.
f(4)= What does this value mean?
(c) It is estimated that in 2015 there were 3.2 billion users. How does the model compare with these findings?
Explanation / Answer
standard exponential equation is given by
y = Ao e^kt
from two points (0, 2.2) and ( 3 , 2.9)
Ao = 2.2
2.9 = 2.2 e^(3k)
2.9/2.2 = e^3k
k = 0.0921
a) exponential model is
f(t) = 2.2 e^.092 t
b) f(4) = 2.2 e^.092 (4)
= 3.179 billion
number of internet users in 2015 = 3.179 billion
c) actual users were 3.2 billion and according to the model it was 3.179 billion
so, we can say that the model is quiet accurate